High School Math : Solid Geometry

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : How To Find The Volume Of A Cube

A cube has a surface area of  units squared. What is its volume?

Possible Answers:

 units cubed

 units cubed

 units cubed

 units cubed

Correct answer:

 units cubed

Explanation:

Since a cube has  square faces and the surface area of each face is given by multiplying the length of one side of the square face by itself, the equation for the surface area of a cube is , where  is the length of one side of one face (i.e., one edge of the cube). Find the length of one side/edge of the given cube by setting the given surface area equal to :

 units

The volume of a cube is , where  is the length of one of the cube's edges. Substituing the solution to the previous equation for  in the volume equation gives the volume of the cube:

 units cubed

Example Question #61 : Solid Geometry

Find the volume of the following cube:

Length_of_diagonal

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a cube is

,

where  is the side of the cube.

Plugging in our values, we get:

Example Question #61 : Solid Geometry

What is the difference in volume between a sphere with radius x and a cube with a side of 2x? Let π = 3.14

Possible Answers:

5.28x3

8.00x3

4.18x3

3.82x3

6.73x3

Correct answer:

3.82x3

Explanation:

Vcube = s3 = (2x)3 = 8x3

Vsphere = 4/3 πr3 = 4/3•3.14•x3 = 4.18x

 

Example Question #151 : Geometry

The density of gold is and the density of glass is .  You have a gold cube that is  in length on each side.  If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?

Possible Answers:

Correct answer:

Explanation:

Weight = Density * Volume

Volume of Gold Cube = side3= x3

Weight of Gold = 16 g/cm3 * x3

Weight of Glass = 3/cm3  * side3

Set the weight of the gold equal to the weight of the glass and solve for the side length:

16* x3 = 2  * side3

side3 = 16/2* x3 =  8 x3

Take the cube root of both sides:

side = 2x

Example Question #37 : Solid Geometry

A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?

Possible Answers:

Correct answer:

Explanation:

If we let  represent the length of an edge on the smaller cube, its volume is .

The larger cube has edges three times as long, so the length can be represented as . The volume is , which is .

The large cube's volume of  is 27 times as large as the small cube's volume of .

 

Example Question #1 : How To Find The Volume Of A Cube

If a cube has its edges increased by a factor of 5, what is the ratio of the new volume to the old volume?

Possible Answers:

Correct answer:

Explanation:

A cubic volume is . Let the original sides be 1, so that the original volume is 1. Then find the volume if the sides measure 5.  This new volume is 125.  Therefore, the ratio of new volume to old volume is 125: 1.

Example Question #62 : Solid Geometry

A cube has a side length of  meters. What is the volume of the cube? 

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a cube is: 

Since the length of one side is  meters, the volume of the cube is: 

 meters cubed. 

Example Question #61 : Solid Geometry

If the length of the side of a cube is , which expression represents the volume of the cube?

Possible Answers:

none of the other answers

Correct answer:

Explanation:

The formula for the volume of the cube is 

Plugging that into Volume equation, we find  and 

 

Thus, the answer is 512x6

Example Question #1 : How To Find The Volume Of A Cube

A tank measuring 3in wide by 5in deep is 10in tall.  If there are two cubes with 2in sides in the tank, how much water is needed to fill it?

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Pyramids

What is the volume of a pyramid with a height of  and a square base with a side length of ?

Possible Answers:

Correct answer:

Explanation:

To find the volume of a pyramid we must use the equation

 

We must first solve for the area of the square using

We plug in  and square it to get 

We then plug our answer into the equation for the pyramid with the height to get

 

We multiply the result to get our final answer for the volume of the pyramid

 .

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