3-Dimensional Geometry

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GED Math › 3-Dimensional Geometry

Questions 1 - 10
1

Find the volume of a cube with a width of 11in.

Explanation

To find the volume of a cube, we will use the following formula:

where l is the length, w is the width, and h is the height of the cube.

Now, we know the width of the cube is 11in. Because it is a cube, all widths/lengths/etc are the same. Therefore, the length and the height are also 11in. So, we substitute. We get

2

Find the volume of a cube with a width of 11in.

Explanation

To find the volume of a cube, we will use the following formula:

where l is the length, w is the width, and h is the height of the cube.

Now, we know the width of the cube is 11in. Because it is a cube, all widths/lengths/etc are the same. Therefore, the length and the height are also 11in. So, we substitute. We get

3

Cone_1

Above is a diagram of a conic tank that holds a city's water supply.

The city wishes to completely repaint the exterior of the tank - sides and base. The paint it wants to use covers 40 square meters per gallon. Also, to save money, the city buys the paint in multiples of 25 gallons.

How many gallons will the city purchase in order to paint the tower?

Explanation

The surface area of a cone with radius and slant height is calculated using the formula .

Substitute 35 for and 100 for to find the surface area in square meters:

square meters.

The paint covers 40 square meters per gallon, so the city needs

gallons of paint.

Since the city buys the paint in multiples of 25 gallons, it will need to buy the next-highest multiple of 25, or 375 gallons.

4

Cone_1

Above is a diagram of a conic tank that holds a city's water supply.

The city wishes to completely repaint the exterior of the tank - sides and base. The paint it wants to use covers 40 square meters per gallon. Also, to save money, the city buys the paint in multiples of 25 gallons.

How many gallons will the city purchase in order to paint the tower?

Explanation

The surface area of a cone with radius and slant height is calculated using the formula .

Substitute 35 for and 100 for to find the surface area in square meters:

square meters.

The paint covers 40 square meters per gallon, so the city needs

gallons of paint.

Since the city buys the paint in multiples of 25 gallons, it will need to buy the next-highest multiple of 25, or 375 gallons.

5

A regular icosahedron has twenty congruent faces, each of which is an equilateral triangle.

A given regular icosahedron has edges of length two inches. Give the total surface area of the icosahedron.

Explanation

The area of an equilateral triangle is given by the formula

.

Since there are twenty equilateral triangles that comprise the surface of the icosahedron, the total surface area is

.

Substitute :

square inches.

6

A regular icosahedron has twenty congruent faces, each of which is an equilateral triangle.

A given regular icosahedron has edges of length two inches. Give the total surface area of the icosahedron.

Explanation

The area of an equilateral triangle is given by the formula

.

Since there are twenty equilateral triangles that comprise the surface of the icosahedron, the total surface area is

.

Substitute :

square inches.

7

Find the surface area of a sphere with a radius of 8in.

Explanation

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 8in.

Knowing this, we can substitute into the formula. We get

8

A regular octahedron has eight congruent faces, each of which is an equilateral triangle.

A given octahedron has edges of length three inches. Give the total surface area of the octahedron.

Explanation

The area of an equilateral triangle is given by the formula

.

Since there are eight equilateral triangles that comprise the surface of the octahedron, the total surface area is

.

Substitute :

square inches.

9

Find the surface area of a sphere with a radius of 8in.

Explanation

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 8in.

Knowing this, we can substitute into the formula. We get

10

A regular octahedron has eight congruent faces, each of which is an equilateral triangle.

A given octahedron has edges of length three inches. Give the total surface area of the octahedron.

Explanation

The area of an equilateral triangle is given by the formula

.

Since there are eight equilateral triangles that comprise the surface of the octahedron, the total surface area is

.

Substitute :

square inches.

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