High School Math : Solid Geometry

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1871 : High School Math

Find the surface area of the following polyhedron.

Ice_cream_cone

Possible Answers:

Correct answer:

Explanation:

The formula for the surface area of the polyhedron is:

Where  is the radius of the cone,  is the slant height of the cone, and  is the radius of the sphere

 

Use the formula for a  triangle to find the radius and slant height:

 

Plugging in our values, we get:

Example Question #1 : How To Find The Surface Area Of A Polyhedron

Find the surface area of the following polyhedron.

Dome

Possible Answers:

Correct answer:

Explanation:

The formula for the surface area of the polyhedron is:

where  is the radius of the cone,  is the slant height of the cone,  is the radius of the cylinder, and  is the height of the cylinder.

 

Use the formula for a  triangle to find the length of the radius:

 

Plugging in our values, we get:

Example Question #1 : How To Find The Surface Area Of A Polyhedron

Find the surface area of the following polyhedron.

Ice_cream_cone

Possible Answers:

Correct answer:

Explanation:

The formula for the surface area of a polyhedron is:

where  is the radius of the polyhedron and  is the slant height of the cone.

 

Use the formula for a  triangle to find the length of the radius:

 

Plugging in our values, we get:

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

Find the volume of the following half cylinder.

Half_cylinder

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a half-cylinder is:

where  is the radius of the base and  is the length of the height.

 

Plugging in our values, we get:

Example Question #21 : Solid Geometry

Find the volume of the following polyhedron.

Ice_cream_cone

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of the polyhedron is:

Where  is the radius of the cone,  is the height of the cone, and  is the radius of the sphere.

 

Use the formula for a  triangle to find the length of the radius:

 

Plugging in our values, we get:

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

Find the volume of the following polyhedron.

Dome

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of the polyhedron is:

where  is the radius of the cone,  is the height of the cone,  is the radius of the cylinder, and  is the height of the cylinder.

 

Use the formula for a  triangle to find the length of the radius and height of the cone:

 

Plugging in our values, we get:

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

Find the volume of the following polyhedron.

Ice_cream_cone

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of the polyhedron is:

where  is the radius of the polyhedron and  is the height of the cone.

 

Use the formula for a  triangle to find the length of the radius and height:

 

Plugging in our values, we get:

Example Question #1 : How To Find The Length Of An Edge Of A Cube

Our backyard pool holds 10,000 gallons.  Its average depth is 4 feet deep and it is 10 feet long.  If there are 7.48 gallons in a cubic foot, how wide is the pool? 

Possible Answers:

133 ft  

100 ft  

 33  ft   

7.48 ft  

30 ft  

Correct answer:

 33  ft   

Explanation:

There are 7.48 gallons in cubic foot. Set up a ratio:

1 ft3 / 7.48 gallons = x cubic feet / 10,000 gallons

Pool Volume = 10,000 gallons = 10,000 gallons * (1 ft3/ 7.48 gallons) = 1336.9 ft3

Pool Volume = 4ft x 10 ft x WIDTH = 1336.9 cubic feet

Solve for WIDTH:

4 ft x 10 ft x WIDTH = 1336.9 cubic feet

WIDTH = 1336.9 / (4 x 10) = 33.4 ft

Example Question #1 : How To Find The Length Of An Edge Of A Cube

A cube has a volume of 64cm3. What is the area of one side of the cube?

Possible Answers:

4cm

4cm2

16cm2

16cm3

16cm

Correct answer:

16cm2

Explanation:

The cube has a volume of 64cm3, making the length of one edge 4cm (4 * 4 * 4 = 64).

So the area of one side is 4 * 4 = 16cm2

Example Question #1 : How To Find The Length Of An Edge Of A Cube

Given that the suface area of a cube is 72, find the length of one of its sides. 

Possible Answers:

Correct answer:

Explanation:

The standard equation for surface area is 

where  denotes side length. Rearrange the equation in terms of  to find the length of a side with the given surface area:

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