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

The volume of a rectangular prism is .

We are told that the shortest edge is 3. Let us call this the height.

We now have , or .

Now we replace variables by known values:

Now we have:

We have thus determined that the other two edges of the rectangular prism will be 4 and 12. We now need to find the longest diagonal. This is equal to:

If you do not remember how to find this directly, you can also do it in steps. You first find the diagonal across one of the sides (in the plane), by using the Pythagorean Theorem. For example, we choose the side with edges 3 and 4. This diagonal will be:

We then use a plane with one side given by the diagonal we just found (length 5) and the other given by the distance of the 3rd edge (length 12).

This diagonal is then .

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,

.

First, you will want to create a pyramid with measurements that are easy to calculate. So, let's say that we have pyramid with a base edge of 10 inches and a height of 10 inches.

So the volume of the original pyramid would be equal to

The volume of the altered pyramid would be equal to:

To find the relationship between the volume of the altered pyramid relative to the volume of the original pyramid, divide the altered volume by the original volume.

The new volume is 59% of the original volume, which means there was a 41% decrease in volume.

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

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,

.

Write the formula to find the surface area of a sphere.

Substitute the area and solve for the radius.

The diameter is double the radius.

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 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,

.

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.