How to find the volume of a sphere - SSAT Upper Level Quantitative

Card 1 of 28

Didn't Know

Knew It

1 of 2019 left

Question

What is the volume of a sphere with diameter 12 feet?

Tap to reveal answer

Answer

The radius of the sphere is half the diameter, or 6 feet; use the formula

$V= $\frac{4}{3}$ \pi $r^{3}$$ .

Setting :

$V= $\frac{4}{3}$ \pi \cdot $6^{3}$ \approx904.8 $ft^{3}$$

← Didn't Know|Knew It →

Question

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

Tap to reveal answer

Answer

The volume of a sphere, given its radius, is

$V = $\frac{4\pi $r^{3}$$}{3}$

Set , solve for , and double that to get the diameter.

$1,000= $\frac{4\pi $r^{3}$$}{3}$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

← Didn't Know|Knew It →

Question

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

Tap to reveal answer

Answer

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}$\pi $r^3$$

where is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be $10\div 2=5$ meters. Now we can get:

$Volume=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi\times $5^3$=\frac{4}{3}$\times \pi \times 125\approx 523.6 $m^3$$

← Didn't Know|Knew It →

Question

The volume of a sphere is 1000 cubic inches. What is the diameter of the sphere.

Tap to reveal answer

Answer

The volume of a sphere is:

$Volume=\frac{4}{3}$\pi $r^3$$

Where is the radius of the sphere. We know the volume and can solve the formula for :

$Volume=\frac{4}{3}$\pi $r^3$=1000\Rightarrow $r^3$=\frac{3\times1000 }{4\pi}$\approx 238.85\Rightarrow r\approx 6.2$ inches

So we can get:

$Diameter=2r=2\times 6.2=12.4inches$

← Didn't Know|Knew It →

Question

The diameter of a sphere is . Give the volume of the sphere in terms of .

Tap to reveal answer

Answer

The diameter of a sphere is so the radius of the sphere would be $6t\div 2=3t$

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi \times $(3t)^3$=\frac{4}{3}$\pi\times $27t^3$\Rightarrow Volume=36\pi $t^3$$

← Didn't Know|Knew It →

Question

A sphere has a diameter of inches. What is the volume of this sphere?

Tap to reveal answer

Answer

To find the volume of a sphere, use the following formula:

$\text{Volume}$=\frac{4}{3}$\pi\times $r^3$ , where is the radius of the sphere.

Now, because we are given the diameter of the sphere, divide that value in half to find the radius.

$r=10\div2=5$

Now, plug this value into the volume equation.

$\text{Volume}$=\frac{4}{3}$\pi\times $5^3$

$$\text{Volume}$=\frac{4}{3}$\pi\times 125$

$$\text{Volume}$=\frac{500}{3}$\pi=523.6$

← Didn't Know|Knew It →

Question

What is the volume of a sphere with a diameter of ?

Tap to reveal answer

Answer

Write the formula for the volume of the sphere.

$V=\frac{4}{3}$\pi $r^3$$

The radius is half the diameter, which is five. Substitute the value.

$V=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi $(5)^3$=\frac{4}{3}$\pi (125)= $\frac{500}{3}$\pi$

← Didn't Know|Knew It →

Question

What is the volume of a sphere with diameter 12 feet?

Tap to reveal answer

Answer

The radius of the sphere is half the diameter, or 6 feet; use the formula

$V= $\frac{4}{3}$ \pi $r^{3}$$ .

Setting :

$V= $\frac{4}{3}$ \pi \cdot $6^{3}$ \approx904.8 $ft^{3}$$

← Didn't Know|Knew It →

Question

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

Tap to reveal answer

Answer

The volume of a sphere, given its radius, is

$V = $\frac{4\pi $r^{3}$$}{3}$

Set , solve for , and double that to get the diameter.

$1,000= $\frac{4\pi $r^{3}$$}{3}$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

← Didn't Know|Knew It →

Question

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

Tap to reveal answer

Answer

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}$\pi $r^3$$

where is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be $10\div 2=5$ meters. Now we can get:

$Volume=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi\times $5^3$=\frac{4}{3}$\times \pi \times 125\approx 523.6 $m^3$$

← Didn't Know|Knew It →

Question

The volume of a sphere is 1000 cubic inches. What is the diameter of the sphere.

Tap to reveal answer

Answer

The volume of a sphere is:

$Volume=\frac{4}{3}$\pi $r^3$$

Where is the radius of the sphere. We know the volume and can solve the formula for :

$Volume=\frac{4}{3}$\pi $r^3$=1000\Rightarrow $r^3$=\frac{3\times1000 }{4\pi}$\approx 238.85\Rightarrow r\approx 6.2$ inches

So we can get:

$Diameter=2r=2\times 6.2=12.4inches$

← Didn't Know|Knew It →

Question

The diameter of a sphere is . Give the volume of the sphere in terms of .

Tap to reveal answer

Answer

The diameter of a sphere is so the radius of the sphere would be $6t\div 2=3t$

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi \times $(3t)^3$=\frac{4}{3}$\pi\times $27t^3$\Rightarrow Volume=36\pi $t^3$$

← Didn't Know|Knew It →

Question

A sphere has a diameter of inches. What is the volume of this sphere?

Tap to reveal answer

Answer

To find the volume of a sphere, use the following formula:

$\text{Volume}$=\frac{4}{3}$\pi\times $r^3$ , where is the radius of the sphere.

Now, because we are given the diameter of the sphere, divide that value in half to find the radius.

$r=10\div2=5$

Now, plug this value into the volume equation.

$\text{Volume}$=\frac{4}{3}$\pi\times $5^3$

$$\text{Volume}$=\frac{4}{3}$\pi\times 125$

$$\text{Volume}$=\frac{500}{3}$\pi=523.6$

← Didn't Know|Knew It →

Question

What is the volume of a sphere with a diameter of ?

Tap to reveal answer

Answer

Write the formula for the volume of the sphere.

$V=\frac{4}{3}$\pi $r^3$$

The radius is half the diameter, which is five. Substitute the value.

$V=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi $(5)^3$=\frac{4}{3}$\pi (125)= $\frac{500}{3}$\pi$

← Didn't Know|Knew It →

Question

What is the volume of a sphere with diameter 12 feet?

Tap to reveal answer

Answer

The radius of the sphere is half the diameter, or 6 feet; use the formula

$V= $\frac{4}{3}$ \pi $r^{3}$$ .

Setting :

$V= $\frac{4}{3}$ \pi \cdot $6^{3}$ \approx904.8 $ft^{3}$$

← Didn't Know|Knew It →

Question

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

Tap to reveal answer

Answer

The volume of a sphere, given its radius, is

$V = $\frac{4\pi $r^{3}$$}{3}$

Set , solve for , and double that to get the diameter.

$1,000= $\frac{4\pi $r^{3}$$}{3}$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

← Didn't Know|Knew It →

Question

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

Tap to reveal answer

Answer

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}$\pi $r^3$$

where is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be $10\div 2=5$ meters. Now we can get:

$Volume=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi\times $5^3$=\frac{4}{3}$\times \pi \times 125\approx 523.6 $m^3$$

← Didn't Know|Knew It →

Question

The volume of a sphere is 1000 cubic inches. What is the diameter of the sphere.

Tap to reveal answer

Answer

The volume of a sphere is:

$Volume=\frac{4}{3}$\pi $r^3$$

Where is the radius of the sphere. We know the volume and can solve the formula for :

$Volume=\frac{4}{3}$\pi $r^3$=1000\Rightarrow $r^3$=\frac{3\times1000 }{4\pi}$\approx 238.85\Rightarrow r\approx 6.2$ inches

So we can get:

$Diameter=2r=2\times 6.2=12.4inches$

← Didn't Know|Knew It →

Question

The diameter of a sphere is . Give the volume of the sphere in terms of .

Tap to reveal answer

Answer

The diameter of a sphere is so the radius of the sphere would be $6t\div 2=3t$

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi \times $(3t)^3$=\frac{4}{3}$\pi\times $27t^3$\Rightarrow Volume=36\pi $t^3$$

← Didn't Know|Knew It →

Question

A sphere has a diameter of inches. What is the volume of this sphere?

Tap to reveal answer

Answer

To find the volume of a sphere, use the following formula:

$\text{Volume}$=\frac{4}{3}$\pi\times $r^3$ , where is the radius of the sphere.

Now, because we are given the diameter of the sphere, divide that value in half to find the radius.

$r=10\div2=5$

Now, plug this value into the volume equation.

$\text{Volume}$=\frac{4}{3}$\pi\times $5^3$

$$\text{Volume}$=\frac{4}{3}$\pi\times 125$

$$\text{Volume}$=\frac{500}{3}$\pi=523.6$

← Didn't Know|Knew It →

Knew It

How to find the volume of a sphere - SSAT Upper Level Quantitative

What is the volume of a sphere with diameter 12 feet?

The radius of the sphere is half the diameter, or 6 feet; use the formula . Setting :

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

The volume of a sphere, given its radius, is Set , solve for , and double that to get the diameter. The diameter is twice this, or 12.4 yards.

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

The volume enclosed by a sphere is given by the formula: where is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be meters. Now we can get:

The volume of a sphere is 1000 cubic inches. What is the diameter of the sphere.

The volume of a sphere is: Where is the radius of the sphere. We know the volume and can solve the formula for : inches So we can get:

The diameter of a sphere is . Give the volume of the sphere in terms of .

The diameter of a sphere is so the radius of the sphere would be The volume enclosed by a sphere is given by the formula:

A sphere has a diameter of inches. What is the volume of this sphere?

To find the volume of a sphere, use the following formula: , where is the radius of the sphere. Now, because we are given the diameter of the sphere, divide that value in half to find the radius. Now, plug this value into the volume equation.

What is the volume of a sphere with a diameter of ?

Write the formula for the volume of the sphere. The radius is half the diameter, which is five. Substitute the value.

What is the volume of a sphere with diameter 12 feet?

The radius of the sphere is half the diameter, or 6 feet; use the formula . Setting :

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

The volume of a sphere, given its radius, is Set , solve for , and double that to get the diameter. The diameter is twice this, or 12.4 yards.

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

The volume enclosed by a sphere is given by the formula: where is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be meters. Now we can get:

The volume of a sphere is 1000 cubic inches. What is the diameter of the sphere.

The volume of a sphere is: Where is the radius of the sphere. We know the volume and can solve the formula for : inches So we can get:

The diameter of a sphere is . Give the volume of the sphere in terms of .

The diameter of a sphere is so the radius of the sphere would be The volume enclosed by a sphere is given by the formula:

A sphere has a diameter of inches. What is the volume of this sphere?

To find the volume of a sphere, use the following formula: , where is the radius of the sphere. Now, because we are given the diameter of the sphere, divide that value in half to find the radius. Now, plug this value into the volume equation.

What is the volume of a sphere with a diameter of ?

Write the formula for the volume of the sphere. The radius is half the diameter, which is five. Substitute the value.

What is the volume of a sphere with diameter 12 feet?

The radius of the sphere is half the diameter, or 6 feet; use the formula . Setting :

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

The volume of a sphere, given its radius, is Set , solve for , and double that to get the diameter. The diameter is twice this, or 12.4 yards.

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

The volume enclosed by a sphere is given by the formula: where is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be meters. Now we can get:

The volume of a sphere is 1000 cubic inches. What is the diameter of the sphere.

The volume of a sphere is: Where is the radius of the sphere. We know the volume and can solve the formula for : inches So we can get:

The diameter of a sphere is . Give the volume of the sphere in terms of .

The diameter of a sphere is so the radius of the sphere would be The volume enclosed by a sphere is given by the formula:

A sphere has a diameter of inches. What is the volume of this sphere?

To find the volume of a sphere, use the following formula: , where is the radius of the sphere. Now, because we are given the diameter of the sphere, divide that value in half to find the radius. Now, plug this value into the volume equation.

The radius of the sphere is half the diameter, or 6 feet; use the formula

$V= $\frac{4}{3}$ \pi $r^{3}$$ .

Setting :

$V= $\frac{4}{3}$ \pi \cdot $6^{3}$ \approx904.8 $ft^{3}$$

The volume of a sphere, given its radius, is

$V = $\frac{4\pi $r^{3}$$}{3}$

Set , solve for , and double that to get the diameter.

$1,000= $\frac{4\pi $r^{3}$$}{3}$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

The diameter of a sphere is so the radius of the sphere would be $6t\div 2=3t$

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi \times $(3t)^3$=\frac{4}{3}$\pi\times $27t^3$\Rightarrow Volume=36\pi $t^3$$

Write the formula for the volume of the sphere.

$V=\frac{4}{3}$\pi $r^3$$

The radius is half the diameter, which is five. Substitute the value.

$V=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi $(5)^3$=\frac{4}{3}$\pi (125)= $\frac{500}{3}$\pi$

The radius of the sphere is half the diameter, or 6 feet; use the formula

$V= $\frac{4}{3}$ \pi $r^{3}$$ .

Setting :

$V= $\frac{4}{3}$ \pi \cdot $6^{3}$ \approx904.8 $ft^{3}$$

The volume of a sphere, given its radius, is

$V = $\frac{4\pi $r^{3}$$}{3}$

Set , solve for , and double that to get the diameter.

$1,000= $\frac{4\pi $r^{3}$$}{3}$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

The diameter of a sphere is so the radius of the sphere would be $6t\div 2=3t$

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi \times $(3t)^3$=\frac{4}{3}$\pi\times $27t^3$\Rightarrow Volume=36\pi $t^3$$

Write the formula for the volume of the sphere.

$V=\frac{4}{3}$\pi $r^3$$

The radius is half the diameter, which is five. Substitute the value.

$V=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi $(5)^3$=\frac{4}{3}$\pi (125)= $\frac{500}{3}$\pi$

The radius of the sphere is half the diameter, or 6 feet; use the formula

$V= $\frac{4}{3}$ \pi $r^{3}$$ .

Setting :

$V= $\frac{4}{3}$ \pi \cdot $6^{3}$ \approx904.8 $ft^{3}$$

The volume of a sphere, given its radius, is

$V = $\frac{4\pi $r^{3}$$}{3}$

Set , solve for , and double that to get the diameter.

$1,000= $\frac{4\pi $r^{3}$$}{3}$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

The diameter of a sphere is so the radius of the sphere would be $6t\div 2=3t$

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}$\pi $r^3$=\frac{4}{3}$\pi \times $(3t)^3$=\frac{4}{3}$\pi\times $27t^3$\Rightarrow Volume=36\pi $t^3$$