All High School Math Resources
Example Questions
Example Question #2 : How To Find The Surface Area Of A Cube
What is the surface area of a cube with a diagonal of ?
A few facts need to be known to solve this problem. Observe that the diagonal of the square face of the cube cuts it into two right isosceles triangles; therefore, the length of a side of the square to its diagonal is the same as an isosceles right triangle's leg to its hypotenuse: .
Rearrange an solve for .
Now, solve for the area of the cube using the formula .
Example Question #1 : How To Find The Surface Area Of A Cube
This figure is a cube with one face having an area of 16 in2.
What is the surface area of the cube (in2)?
The surface area of a cube is the sum of the area of each face. Since there are 6 faces on a cube, the surface area of the entire cube is .
Example Question #2 : How To Find The Surface Area Of A Cube
A cube has a height of 4 feet. What is the surface area of the cube in feet?
To find the surface area of a cube, square the length of one edge and multiply the result by six:
Example Question #16 : Cubes
The side length of a particular cube is . What is the surface area of this cube?
To find the surface of a cube, use the standard equation:
where denotes the side length.
Plug in the given value for to find the answer:
Example Question #17 : Cubes
Sarah is wrapping a birthday present. The box is a cube with sides of . At a minimum, how many square feet of wrapping paper will she need?
Remember, .
For a cube:
Thus .
Example Question #41 : Solid Geometry
Example Question #42 : Solid Geometry
Find the surface area of the following cube:
The formula for the surface area of a cube is
,
where is the length of the side.
Plugging in our values, we get:
Example Question #1 : How To Find The Surface Area Of A Cube
The side of a cube has a length of . What is the total surface area of the cube?
A cube has 6 faces. The area of each face is found by squaring the length of the side.
Multiply the area of one face by the number of faces to get the total surface area of the cube.
Example Question #2 : How To Find The Surface Area Of A Cube
What is the surface area of a cube if its height is 3 cm?
The area of one face is given by the length of a side squared.
The area of 6 faces is then given by six times the area of one face: 54 cm2.
Example Question #583 : Geometry
A sphere with a volume of is inscribed in a cube, as shown in the diagram below.
What is the surface area of the cube, in ?
We must first find the radius of the sphere in order to solve this problem. Since we already know the volume, we will use the volume formula to do this.
With the radius of the sphere in hand, we can now apply it to the cube. The radius of the sphere is half the distance from the top to the bottom of the cube (or half the distance from one side to another). Therefore, the radius represents half of a side length of a square. So in this case
The formula for the surface area of a cube is:
The surface area of the cube is