To find the surface area of a sphere, we will use the following formula:

where r is the radius of the sphere.

Now, we know the radius of the sphere is 10in. So, we will substitute. We get

Write the formula for the surface area of a cube.

Substitute the side into the equation.

The answer is:  

Recall the formula to find the surface area of a cube:

Start by solving for the length of a side of the cube.

Now recall how to find the volume of a cube:

Plug in the found side length to find the volume.

Write the formula for the surface area of a square.

We will determine the areas of the 6 faces of the square.

The answer is:  

You are given a small cube with an edge length of . Find the surface area of the cube.

A cube has six faces, each with an area of side squared. Thus, we use the formula:

Now, we plug in our side length and solve.

You are given a chest with the following dimensions: 3' X 2' X 1.5'. 

What is the surface area of the chest?

To find the surface area of a rectangular prism, use the following formula:

Where l, h and w are length, width and height.

So, let's plug in our values and solve for SA.

So, our answer is 

You have a cube with surface area of .

What is the area of one face of the cube?

To find the surface area of a cube, we use the following formula:

Where s squared gives us the area of one face. We multiply by 6 because there are six faces.

So, we can rewrite our above formula to get:

So, if we plug in our given surface area, we can find the area of one face.

So, our answer is

Start by finding the volume of the paint can. Recall how to find the volume of a cylinder:

, where  is the radius and  is the height.

Plug in the given radius and height to find the volume of the paint can.

Now, divide the total volume of paint made by the factory in a day by the volume of an individual paint can to determine how many cans will be filled.

Since the question asks for the number of complete cans that will be filled, the factory can only fill  cans a day.

Consider a tube which is 3 ft wide and 18 ft long.

Find the surface area of the largest sphere which could fit within the tube described above.

Okay, so we need to find the surface area of a sphere. To do so, we need the following formula:

Now, you're probably thinking, "How do we find our radius?" Well, we need to look at our tube.

The largest sphere which will fit within the tube is the same thing as a sphere with diameter equal to the tube's diameter.

In this case, the diameter of the tube is 3 ft. This means our sphere's diameter is also 3 feet.

If our diameter is 3 ft, then our radius is half of that- 1.5 ft.

So, with a 1.5 ft radius, our surface area becomes:

So, leaving our answer in terms of pi, we get:

Find the surface area of a rectangular prism with the following dimensions: 6 ft by 12 ft by 4 ft.

To find the surface area of a rectangular prism, we essentially need to add up the area of all the sides. To do so, use the following formula:

Where l, w, and h are our length, height, and width. 

We simply need to plug in our given measurements and solve

So, our surface area is