How to find the surface area of a cube - SAT Math

The equation for surface area of the original cube is 6s2. If the sides all double in length the new equation is 6(2s)2 or 6 * 4s2. This makes the new surface area 4x that of the old. 4x10 = 40m2

This problem is relatively simple. We know that the volume of a cube is equal to s3, where s is the length of a given side of the cube. Therefore, to find our dimensions, we merely have to solve s3 = 1728. Taking the cubed root, we get s = 12.

Since the sides of a cube are all the same, the surface area of the cube is equal to 6 times the area of one face. For our dimensions, one face has an area of 12 * 12 or 144 in2. Therefore, the total surface area is 6 * 144 = 864 in2.

If broken down into parts, this is an easy problem. It is first necessary to isolate the dimensions of the walls. If the room is 9 ft high, we know 18 x 15 designates the area of the floor and ceiling. Based on this, we know that the room has the following dimensions for the walls: 18 x 9 and 15 x 9. Since there are two of each, we can calculate the total area of walls - ignoring doors and windows - by doubling the sum of these two areas:

2 * (18 * 9 + 15 * 9) = 2 * (162 + 135) = 2 * 297 = 594 ft2

Now, we merely need to calculate the area "taken out" of the walls:

For the door: 3 * 7 = 21 ft2

For the windows: 2 * (2 * 5) = 20 ft2

The total wall space is therefore: 594 – 21 – 20 = 553 ft2

If broken down into parts, this is an easy problem. It is first necessary to isolate the dimensions of the walls. If the room is 10ft high, we know 23 x 17 designates the area of the floor and ceiling. Based on this, we know that the room has the following dimensions for the walls: 23 x 10 and 17 x 10. Since there are two of each, we can calculate the total area of walls - ignoring doors and windows - by doubling the sum of these two areas:

2 * (23 * 10 + 17 * 10) = 2 * (230 + 170) = 2 * 400 = 800 ft2

Now, we merely need to calculate the area "taken out" of the walls:

For the door: 2.5 * 8 = 20 ft2

For the windows: 3 * 6 = 18 ft2

The total wall space is therefore: 800 – 20 – 18 = 762 ft2

Now, if one can of paint covers 57 ft2, we calculate the number of cans necessary by dividing the total exposed area by 57: 762/57 = (approx.) 13.37.

Since we cannot buy partial cans, we must purchase 14 cans.

A cube with a side length of 25m has a surface area of:

25m * 25m * 6 = 3,750 m2

(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6_s_2.)

Each square tile has an area of 5 m2.

Therefore, the total number of square tiles needed to fully cover the surface of the cube is:

3,750m2/5m2 = 750

Note: the volume of a cube with side length s is equal to _s_3. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:

s3/n3

To begin, we need to solve for the dimensions of the cone.

The basic form for the volume of a cone is: V = (1/3)πr_2_h

Using our data, we know that h = 2r because the height of the cone matches its diameter (based on the prompt).

486_π_ = (1/3)πr_2 * 2_r = (2/3)_πr_3

Multiply both sides by (3/2_π_): 729 = _r_3

Take the cube root of both sides: r = 9

Note that this is in feet. The answers are in square inches. Therefore, convert your units to inches: 9 * 12 = 108, then add 3 inches to this: 108 + 3 = 111 inches.

The surface area of the cube is defined by: A = 6 * _s_2, or for our data, A = 6 * 1112 = 73,926 in2

The volume of a cube is given by the formula V = , where V is the volume, and s is the length of each side. We can set V to 216 and then solve for s.

In order to find s, we can find the cube root of both sides of the equaton. Finding the cube root of a number is the same as raising that number to the one-third power.

This means the length of the side of the cube is 6. We can use this information to find the surface area of the cube, which is equal to . The formula for surface area comes from the fact that each face of the cube has an area of , and there are 6 faces in a cube.

surface area =

The surface area of the square is 216 square units.

The answer is 216.

The area of one side of the cube is:

A cube has 6 sides, so the total surface area of the cube is

We have a cube with a surface area of 24, which means each side has an area of 4. Therefore, the length of each side is 2. If we double the height, the volume becomes .

Write the formula for the surface area of a cube.

Substitute the side.

The surface area of a cube can be calculated by squaring the sidelength and multiplying by six. The two smallest cubes therefore have surface areas

and

The surface areas form an arithmetic sequence with these two surface areas as the first two terms, so their common difference is

.

The surface area of the largest, or sixth-smallest, cube, is

To solve, simply use the formula for the surface area of a cube. Thus,

To find the surface area of a cube means to find the area around the entire object. In the case of a cube, we will need to find that area of all the sides and the top and bottom. Since a cube has equal side lengths, the area of each side and the area of the top and bottom will all be the same.

Recall that the area for a side of a cube is:

From here there are two approaches one can take.

Approach one:

Add all the areas together.

Approach two:

Use the formula for the surface area of a cube,

In this particular case we are given the side length is 3.

Thus we can find the surface area to be,

by approach one,

and by appraoch two,

.

To solve, simply use the formula for the surface area of a cube.

If you do not remember the formula for the test, it is important to draw a picture or to visually conceptualize it. Remember, when finding area of a square or rectangle, you simply multiply the two side lengths. So for a cube in 3 dimensions, you simply have to multiply those three together.

However, a cube is a special case where all three lengths are the same. Thus,

First, we need the side length of the cube. Given that , where is a side length, we can solve for and set simply by taking the cube root of both sides.

Then we need to remember or realize that the surface area of a cube is because there will be six identical square faces. Plugging in , we get as our answer.

To solve, simply use the formula for the surface area of a cube.

If this is not a formula you have committed to memory, remember that a cube has 6 faces with equal area. So, start by calculating the surface area of one side (64) and add it 6 times. Thus,

You own a Rubik's cube with a volume of . What is the surface area of the cube?

To solve for edge length, think of the volume of a cube formula:

Now, we have the volume, so just rearrange it to solve for side length:

Next, recall the surface area of a cube formula:

Plug in and simplify to get:

The equation for surface area of the original cube is 6s2. If the sides all double in length the new equation is 6(2s)2 or 6 * 4s2. This makes the new surface area 4x that of the old. 4x10 = 40m2

This problem is relatively simple. We know that the volume of a cube is equal to s3, where s is the length of a given side of the cube. Therefore, to find our dimensions, we merely have to solve s3 = 1728. Taking the cubed root, we get s = 12.

Since the sides of a cube are all the same, the surface area of the cube is equal to 6 times the area of one face. For our dimensions, one face has an area of 12 * 12 or 144 in2. Therefore, the total surface area is 6 * 144 = 864 in2.

If broken down into parts, this is an easy problem. It is first necessary to isolate the dimensions of the walls. If the room is 9 ft high, we know 18 x 15 designates the area of the floor and ceiling. Based on this, we know that the room has the following dimensions for the walls: 18 x 9 and 15 x 9. Since there are two of each, we can calculate the total area of walls - ignoring doors and windows - by doubling the sum of these two areas:

2 * (18 * 9 + 15 * 9) = 2 * (162 + 135) = 2 * 297 = 594 ft2

Now, we merely need to calculate the area "taken out" of the walls:

For the door: 3 * 7 = 21 ft2

For the windows: 2 * (2 * 5) = 20 ft2

The total wall space is therefore: 594 – 21 – 20 = 553 ft2