GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #11 : Volume Of A Rectangular Solid

Tammy has an aquarium in the shape of a rectangular prism. The aquarium has the following dimensions: . In order for her to properly clean the aquarium, she must remove two-thirds of the water in the aquarium. In cubic inches, how much water must she remove?

Possible Answers:

Correct answer:

Explanation:

Start by finding the volume of the rectangular prism.

For the given dimensions,

Since Tammy needs to remove two-thirds of the water, we will need to find two-thirds of the volume.

Tammy must remove  of water.

Example Question #1551 : Ged Math

If a brick is a rectangular sold, what is its volume if its base area is 4, and the height is 5?

Possible Answers:

Correct answer:

Explanation:

Write the formula for the area of a rectangular solid.

The base area consists of , which means we can substitute the area as replacement of the two variables.

The answer is:  

Example Question #41 : 3 Dimensional Geometry

For an art project, Amy needs to paint a rectangular box with the dimensions  red, blue, and yellow. Each color must take up one-third of the painted surface. In square inches, how much blue paint is needed?

Possible Answers:

Correct answer:

Explanation:

Since Amy is painting the outside of a box, we will need to find the surface area of the box.

Recall how to find the surface area of a rectangular prism:

, where  is the width,  is the height, and  is the length.

Because we are only interested in the amount of blue paint that Amy will be painting, we know that we will need to find one-third of the surface area.

Plug in the dimensions of the box to find the area of the blue paint.

Example Question #1553 : Ged Math

A rectangular prism has as its three dimensions , and . Give its volume in terms of .

Possible Answers:

Correct answer:

Explanation:

The volume of a rectangular prism is equal to the product of its three dimensions, so here,

Apply the distribution property, multiplying  by each of the expressions in the parentheses:

Example Question #42 : 3 Dimensional Geometry

You are building a metal crate to hold fishing equipment. If the crate will be 1.5 ft long, 2 feet tall, and 5 feet wide, what will its volume be?

Possible Answers:

Correct answer:

Explanation:

You are building a metal crate to hold fishing equipment. If the crate will be 1.5 ft long, 2 feet tall, and 5 feet wide, what will its volume be?

We are asked to find the volume of a rectangular solid. In this case it is a metal crate, but it is essentially a rectangular solid. To find its volume, use the following formula:

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

 

 

Example Question #41 : 3 Dimensional Geometry

Prism

One cubic centimeter of pure iron is about  in mass. 

Using this figure, what is the mass, in kilograms, of the above iron bar?

Possible Answers:

Correct answer:

Explanation:

First, convert the dimensions of the prism to centimeters. One meter is equal to 100 centimeters, so multiply by this conversion factor:

The dimensions of the prism are 80 centimeters by 30 centimeters by centimeters; multiply these dimensions to find the volume:

Using the given mass of 7.9 grams per cubic centimeter, multiply:

One kilogram is equal to 1,000 grams, so divide by this conversion factor:

,

the correct mass of the prism.

Example Question #591 : Geometry And Graphs

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

Possible Answers:

Correct answer:

Explanation:

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

To find the volume of a rectangular prism, simply multiply the length by the width by the height.

So, plug in and multiply to get:

So, our answer is:

Coincidentally the same as our surface area

Example Question #592 : Geometry And Graphs

What is the volume of a box with length of 3 feet, width of 5 feet, and height of 2 feet?

Possible Answers:

15 feet squared

12 feet squared 

30 feet squared

10 feet squared

7 feet squared 

Correct answer:

30 feet squared

Explanation:

The equation for the volume of a rectangular prism is

So we simply input our dimensions

Example Question #1 : Volume Of A Cylinder

One cubic foot is equal to (about) 7.5 gallons.

A circular swimming pool has diameter 60 feet and depth five feet throughout. Using the above conversion factor, how many gallons of water does it hold?

Use 3.14 for .

Possible Answers:

Correct answer:

Explanation:

The pool can be seen as a cylinder with depth (or height) 5 feet, and a base with diameter 60 feet - and radius half this, or 30 feet. The capacity of the pool is the volume of this cylinder, which is

 cubic feet.

One cubic foot is equal to 7.5 gallons, so multiply:

 gallons

Example Question #2 : Volume Of A Cylinder

A cylindrical bucket is one foot high and one foot in diameter. It is filled with water, which is then emptied into an empty barrel three feet high and two feet in diameter. What percent of the barrel has been filled?

Possible Answers:

Correct answer:

Explanation:

The volume of a cylinder is 

The bucket has height  and diameter 1, and,subsequently, radius ; its volume is

 cubic feet

The barrel has height  and diameter 2,and, subsequently, radius ; its volume is

 

The volume of the bucket is 

 

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