How to find the volume of a prism - ACT Math

Card 0 of 36

Question

A rectangular box has two sides with the following lengths:

and

If it possesses a volume of $84$ cm$^{3}$ , what is the area of its largest side?

Answer

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$

$A=4\times 7$

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Question

A box's length is twice as long as its width. Its height is the sum of its length and its width. What is the volume of this box if its length is 10 units?

Answer

The formula for the volume of a rectangular prism is , where "" is volume, "" is length, "" is width and "" is height.

We know that and . By rearranging , we get $W=\frac{L}{2}$ . Substituting $\frac{L}{2}$ into the volume equation for and into the same equation for , we get the following:

$V = L \cdot \left(\frac{L}{2}\right)\cdot (L+\left(\frac{L}{2}\right))$

$V = L\cdot \left(\frac{L}{2}\right)\cdot \frac{3L}{2}$

$V = 10 \cdot 5 \cdot 15$

units cubed

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Question

A rectangular prism has the following dimensions:

Length:

Width:

Height:

Find the volume.

Answer

Given that the dimensions are: , , and and that the volume of a rectangular prism can be given by the equation:

$v=l \cdot w \cdot h$ , where is length, is width, and is height, the volume can be simply solved for by substituting in the values.

This final value can be approximated to .

Compare your answer with the correct one above

Question

Solve for the volume of a prism that is 4m by 3m by 8m.

Answer

The volume of the rectangle

so we plug in our values and obtain

.

Compare your answer with the correct one above

Question

A rectangular box has two sides with the following lengths:

and

If it possesses a volume of $84$ cm$^{3}$ , what is the area of its largest side?

Answer

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$

$A=4\times 7$

Compare your answer with the correct one above

Question

A box's length is twice as long as its width. Its height is the sum of its length and its width. What is the volume of this box if its length is 10 units?

Answer

The formula for the volume of a rectangular prism is , where "" is volume, "" is length, "" is width and "" is height.

We know that and . By rearranging , we get $W=\frac{L}{2}$ . Substituting $\frac{L}{2}$ into the volume equation for and into the same equation for , we get the following:

$V = L \cdot \left(\frac{L}{2}\right)\cdot (L+\left(\frac{L}{2}\right))$

$V = L\cdot \left(\frac{L}{2}\right)\cdot \frac{3L}{2}$

$V = 10 \cdot 5 \cdot 15$

units cubed

Compare your answer with the correct one above

Question

A rectangular prism has the following dimensions:

Length:

Width:

Height:

Find the volume.

Answer

Given that the dimensions are: , , and and that the volume of a rectangular prism can be given by the equation:

$v=l \cdot w \cdot h$ , where is length, is width, and is height, the volume can be simply solved for by substituting in the values.

This final value can be approximated to .

Compare your answer with the correct one above

Question

Solve for the volume of a prism that is 4m by 3m by 8m.

Answer

The volume of the rectangle

so we plug in our values and obtain

.

Compare your answer with the correct one above

Question

A rectangular box has two sides with the following lengths:

and

If it possesses a volume of $84$ cm$^{3}$ , what is the area of its largest side?

Answer

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$

$A=4\times 7$

Compare your answer with the correct one above

Question

A box's length is twice as long as its width. Its height is the sum of its length and its width. What is the volume of this box if its length is 10 units?

Answer

The formula for the volume of a rectangular prism is , where "" is volume, "" is length, "" is width and "" is height.

We know that and . By rearranging , we get $W=\frac{L}{2}$ . Substituting $\frac{L}{2}$ into the volume equation for and into the same equation for , we get the following:

$V = L \cdot \left(\frac{L}{2}\right)\cdot (L+\left(\frac{L}{2}\right))$

$V = L\cdot \left(\frac{L}{2}\right)\cdot \frac{3L}{2}$

$V = 10 \cdot 5 \cdot 15$

units cubed

Compare your answer with the correct one above

Question

A rectangular prism has the following dimensions:

Length:

Width:

Height:

Find the volume.

Answer

Given that the dimensions are: , , and and that the volume of a rectangular prism can be given by the equation:

$v=l \cdot w \cdot h$ , where is length, is width, and is height, the volume can be simply solved for by substituting in the values.

This final value can be approximated to .

Compare your answer with the correct one above

Question

Solve for the volume of a prism that is 4m by 3m by 8m.

Answer

The volume of the rectangle

so we plug in our values and obtain

.

Compare your answer with the correct one above

Question

A rectangular box has two sides with the following lengths:

and

If it possesses a volume of $84$ cm$^{3}$ , what is the area of its largest side?

Answer

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$

$A=4\times 7$

Compare your answer with the correct one above

Question

A box's length is twice as long as its width. Its height is the sum of its length and its width. What is the volume of this box if its length is 10 units?

Answer

The formula for the volume of a rectangular prism is , where "" is volume, "" is length, "" is width and "" is height.

We know that and . By rearranging , we get $W=\frac{L}{2}$ . Substituting $\frac{L}{2}$ into the volume equation for and into the same equation for , we get the following:

$V = L \cdot \left(\frac{L}{2}\right)\cdot (L+\left(\frac{L}{2}\right))$

$V = L\cdot \left(\frac{L}{2}\right)\cdot \frac{3L}{2}$

$V = 10 \cdot 5 \cdot 15$

units cubed

Compare your answer with the correct one above

Question

A rectangular prism has the following dimensions:

Length:

Width:

Height:

Find the volume.

Answer

Given that the dimensions are: , , and and that the volume of a rectangular prism can be given by the equation:

$v=l \cdot w \cdot h$ , where is length, is width, and is height, the volume can be simply solved for by substituting in the values.

This final value can be approximated to .

Compare your answer with the correct one above

Question

Solve for the volume of a prism that is 4m by 3m by 8m.

Answer

The volume of the rectangle

so we plug in our values and obtain

.

Compare your answer with the correct one above

Question

A rectangular box has two sides with the following lengths:

and

If it possesses a volume of $84$ cm$^{3}$ , what is the area of its largest side?

Answer

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$

$A=4\times 7$

Compare your answer with the correct one above

Question

A box's length is twice as long as its width. Its height is the sum of its length and its width. What is the volume of this box if its length is 10 units?

Answer

The formula for the volume of a rectangular prism is , where "" is volume, "" is length, "" is width and "" is height.

We know that and . By rearranging , we get $W=\frac{L}{2}$ . Substituting $\frac{L}{2}$ into the volume equation for and into the same equation for , we get the following:

$V = L \cdot \left(\frac{L}{2}\right)\cdot (L+\left(\frac{L}{2}\right))$

$V = L\cdot \left(\frac{L}{2}\right)\cdot \frac{3L}{2}$

$V = 10 \cdot 5 \cdot 15$

units cubed

Compare your answer with the correct one above

Question

A rectangular prism has the following dimensions:

Length:

Width:

Height:

Find the volume.

Answer

Given that the dimensions are: , , and and that the volume of a rectangular prism can be given by the equation:

$v=l \cdot w \cdot h$ , where is length, is width, and is height, the volume can be simply solved for by substituting in the values.

This final value can be approximated to .

Compare your answer with the correct one above

Question

Solve for the volume of a prism that is 4m by 3m by 8m.

Answer

The volume of the rectangle

so we plug in our values and obtain

.

Compare your answer with the correct one above

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