Surface Area and Volume: Solving Surface Area and Volume Problems

Use the prism to complete the statements. The surface area of the cube is ___ cm2. The volume of the cube is ___ cm3.

136 80

Sydney has a rectangular pool as shown in the figure. The pool is 6 feet deep throughout. How much water is needed to fill the pool? 450 ft3 966 ft3 1,416 ft3 2,700 ft3

2,700 ft3

Complete each statement about the prism. The length of the prism is ___ units. The width of the prism is ___ units. The height of the prism is ___ units.

4 3 2

Evan wants to add a flower box at the edge of the garden. The box is 36 inches long, 6 inches wide, and 8 inches high. cube He decides to paint the box. The flower box is open on the top and does not need to be painted. What is the minimum amount of paint he will need? Evan will need enough paint to cover _____in.2. What is the maximum amount of soil he will need to fill the box? The maximum amount of soil is ____ in.3

448 768

Evan is sending a package of some of his produce to his friend in California. The package measures 12 by 9 by 6 inches. He wraps it in brown paper, addresses it, and takes it to the post office to mail. cube How much brown paper will he need to wrap the box? _____ in.2

468

Which questions can be answered by finding the surface area? Check all that apply. How much paint is needed to paint the outside of a birdhouse? How much wallpaper is needed to cover the walls of your room? How much water will it take to fill a rectangular container? How much topsoil can a gardener place in his wheelbarrow? How much fabric is needed to make a pillowcase for a pillow?

How much paint is needed to paint the outside of a birdhouse? How much wallpaper is needed to cover the walls of your room? How much fabric is needed to make a pillowcase for a pillow?

Which question can be answered by finding a volume? How much wrapping paper is needed to wrap that gift? What is the minimum amount of paint needed to cover a jewelry box? If Brad drank all the juice in a juice box, how much juice did he drink? How many square tiles are needed to cover the picture frame?

If Brad drank all the juice in a juice box, how much juice did he drink?

Sasha is filling a rectangular box with ribbon and wants to know the amount of space in the box. Which statement is true about the amount of space inside the box? The space inside the box is the surface area, which is 192 in.2. The space inside the box is the surface area, which is 144 in.2. The space inside the box is the volume, which is 192 in.3. The space inside the box is the volume, which is 144 in.3.

The space inside the box is the volume, which is 144 in.3.

Maria is covering an entire box with 1-in. mosaic tiles and wants to find out how many square inches of mosaic tiles will cover the entire box. Which statement is correct about the amount of mosaic tiles that will cover the entire box? The amount of mosaic tiles covering the box is the surface area, which is 157 in.2. The amount of mosaic tiles covering the box is the surface area, which is 114 in.2. The amount of mosaic tiles covering the box is the volume, which is 157 in.3. The amount of mosaic tiles covering the box is the volume, which is 114 in.3.

The amount of mosaic tiles covering the box is the surface area, which is 157 in.2.

Andrey is making a garden box and wants to know how much dirt is needed to fill the box. Which statement is correct about the amount of dirt that will fill the entire box? The space inside the box is the surface area, which is 128 ft3. The space inside the box is the surface area, which is 192 ft3. The space inside the box is the volume, which is 128 ft3. The space inside the box is the volume, which is 192 ft3.

The space inside the box is the volume, which is 128 ft3.

Surface Area Is:

The total area of the surface of a solid figure. the sum of the area of all of its faces. expressed in square units. found by using a net.

Volume is:

amount of space a solid contains. use lwh of Bh cubic units

Keywords for Surface Area:

cover wrap square units outside total area

Amanda made a jewelry box out of wood. The jewelry box is 7.5 inches long, 5 inches wide, and 3 inches high. Amanda decorates the jewelry box with 1-inch-square gem stickers. cube What is the minimum number of gem stickers needed to completely cover the jewelry box? To answer the question, find the _____. The minimum number of gem stickers is ______.

surface area 150

Evan wants to make a kneeling pad cushion for when he gardens for long periods of time. It will have the dimensions shown. How much fabric should he buy to cover the cushion? Is this a surface area or volume problem? How much fabric will he need? surface area, 336 in.3 surface area, 440 in.2 volume, 336 in.3 volume, 440 in.2

surface area, 440 in.2

What measure should be used to find out how much water is needed to fill a large swimming pool that is 8 feet by 12 feet by 6 feet? lateral area surface area volume

volume

Evan has a storage unit that he keeps all his garden tools in. It measures 4 feet by 3 1/2 feet by 2 feet. What is the maximum amount of supplies that the storage unit can hold? To answer the question, find the ____. The maximum amount of space is ___ ft3.

volume 28

Enzo is filling a pool with water and wants to know how much water is needed to fill the pool. What is the maximum amount of water that the pool can hold? 696 ft2 of water 696 ft3 of water 1,080 ft2 of water 1,080 ft3 of water

1,080 ft3 of water

Eva made a rectangular mattress pad out of material that covered the top and sides of the mattress. How much fabric did Eva use to cover the top and sides of the mattress? 20 ft2 21 ft2 41 ft2 62 ft2

21ft2

Evan enjoys eating fresh fruits and vegetables. This year, he decided to grow his own garden. The diagram shows the dimensions of his garden. He fills his garden with enriched topsoil at a height of 2 inches. How much topsoil does Evan use? __________ cubic inches

2304

Peter built a chest that measures 2 feet by 11 2 feet by 1 foot. He wants to fill the chest with plastic coins. cube What is the maximum amount of space that the chest can hold? The maximum amount of space is ____ cubic feet.

3

Evan grows a lot of tomatoes. He cans the tomatoes and places them in boxes. The diagram shows the dimensions of the boxes. cube What is the maximum space each box can hold? 48 in.3 756 in.3 1,512 in.3 3,888 in.3

3,888 in.3

Tori is sending a birthday gift to her friend out of state and wants to know how much brown paper she will need to cover the box. Which statement is true about the amount of paper Tori will need to cover the entire box? Covering the entire box is the surface area, which is 664 in.2. Covering the entire box is the surface area, which is 1,120 in.2. Covering the entire box is the volume, which is 664 in.3. Covering the entire box is the volume, which is 1,120 in.3.

Covering the entire box is the surface area, which is 664 in.2.

Evan has a box for his garden tools that measures 2 yd by 1.5 yd by 0.75 yd. In order to paint the box, Evan said he needs enough paint to cover 2.25 cubic yards. His work is shown below. Is he correct? Why or why not? V = lwh = 2(1.5)(0.75) = 2.25 yd3

Sample Response: No, his answer is not correct. Evan found the volume. To find the amount of paint needed, he should have found the surface area. Surface area is the sum of the areas of the faces of a solid.

Define surface area and volume. List an example of a situation where you would find surface area and a situation where you would find volume.

Sample Response: Surface area is the sum of the areas of the faces of a solid. It is measured in square units. Volume is the amount of space taken up by a solid. It is measured in cubic units. Surface area would be used to find the amount of wrapping

Define surface area and volume. List an example of a situation where you would find surface area and a situation where you would find volume.

Sample Response: Surface area is the sum of the areas of the faces of a solid. It is measured in square units. Volume is the amount of space taken up by a solid. It is measured in cubic units. Surface area would be used to find the amount of wrapping paper for a gift, and volume would be used to find how much would fit into a box.

Evan places a rectangular birdbath in his garden. The dimensions are 24, 8, and 11 2 in. Explain how to find the maximum amount of water the birdbath can hold. Then find the amount.

Sample Response: Volume is the amount of space inside a solid. So, to find the amount of water the birdbath can hold, find the volume. Multiply length, width, and height: V = (24)(8)(1½) = 288. So, the birdbath can hold a maximum of 288 cubic inches of water.

Missy wants to find the surface area of a snack box in her pantry. Her work is shown below. Steps Missy's Work Step 1 Front or back: 3 x 10 = 30 Left or right: 6 x 10 = 60 Top or bottom: 3 x 6 = 18 Step 2 30 + 60 + 18 Step 3 108 in.² Where, if any, did Missy first make a mistake finding the surface area of the snack box? Step 1: Missy did not calculate the area of the front or back sides correctly. Step 1: Missy did not calculate the area of the left or right sides correctly. Step 2: Missy did not multiply the area of each face by 2 before adding. Step 2: Missy did not multiply the area of each face by 3 before adding.

Step 2: Missy did not multiply the area of each face by 2 before adding.

Which questions can be answered by finding the surface area? Check all that apply. How much soil can the flower box hold? What is the minimum amount of paint needed to cover the garden toolbox? How many packages of seeds can be purchased? How many tiles are needed to cover a garden sculpture? What is the maximum amount of water needed to fill the watering can?

What is the minimum amount of paint needed to cover the garden toolbox? How many tiles are needed to cover a garden sculpture?

Keywords for Volume

fill put in cubic units inside total space