Surface Area and Volume: Finding a Formula for the Volume of a Rectangular Prism

Which expressions show how to calculate the volume of this prism? Check all that apply. 1 + 7(4) 1(4)(7) 4(4)(4) 4 + 1 + 7 4(7)(1) 7(4)(1)

1(4)(7) 4(7)(1) 7(4)(1)

Matt finds a box with dimensions 16 by 8 by 8 inches. What volume can the box hold? Use the formula V = Bh to calculate the volume of the box. The area of the base of the box, B, is __ in.2. The volume of the box is ___ in.3.

128 1024

Matt finds a box with dimensions 16 by 8 by 8 inches. What volume can the box hold? Use the formula V = Bh to calculate the volume of the box. The area of the base of the box, B, is ___ in.2. The volume of the box is ___ in.3.

128 1024

Misaki's fish tank is half full of water because she is cleaning it. The tank is a right rectangular prism with a length of 8 inches, a width of 6 inches, and a height of 6 inches. What is the volume of water in the tank while Misaki is cleaning it? 10 in3 36 in3 144 in3 288 in3

144 in3

What is the volume of the prism?

507m3

Lucas wants to use the box with the greatest volume. Which shipping box should he use?

Box D

Volume

Volume of one layer x number of layers

The formula for volume of a rectangular prism is V = Bh. The variable B stands for the _____. In this prism, B equals ______ cm2. The variable h stands for ______. In this prism, h equals ______ cm. The volume of the prism is ____ cm3.

area of the base 24 height 9 216

What is the volume of the right rectangular prism with a length of 2 millimeters, a width of 4 millimeters, and a height of 8 millimeters? 14 mm3 16 mm3 28 mm3 64 mm3

64 mm3

What is the volume of the prism?

66 cm3

What is the volume of the prism?

672 m3

Felix began finding the volume of the prism using the formula V = Bh. His work is shown. B = 8(24) = 192 cm2 Use the student's work and finish finding the volume of the prism. The volume is ___ cm3.

768

Which shows a correct way to determine the volume of the right rectangular prism? 9 + 1 + 8 = 18 cm3 2(9 + 1 + 8) = 36 cm3 9(3) + 1 = 28 cm3 9(8)(1) = 72 cm3

9(8)(1) = 72 cm3

Tori bought a small container for paper clips in the shape of a right rectangular prism. The container had a height of 8 centimeters, a length of 4 centimeters, and a width of 3 centimeters. What volume can the container hold? 15 cm3 20 cm3 30 cm3 96 cm3

96 cm3

A swimming pool has dimensions of 10 feet by 14 feet by 5 feet. The calculations of five students are shown below. Adina: 70(5) = 350 ft3 Isaac: 14(5)(10) = 700 ft3 Mateo: 10(14) = 140 ft3 Shira: 14(5)(5) = 350 ft3 Zamir: 10(14)(5) = 700 ft3 Which students correctly calculated the volume? Check all that apply. Adina Isaac Mateo Shira Zamir

Isaac Zamir

Anusha needs to find a rectangular container large enough to hold a volume of 130 in.3. Which container should she use? a container with the dimensions 2 by 5 by 10 inches a container with the dimensions 3 by 4 by 10 inches a container with the dimensions 3 by 5 by 10 inches a container with the dimensions 4 by 2 by 10 inches

a container with the dimensions 3 by 5 by 10 inches

The formula for volume of a rectangular prism is V = lwh. The length of the prism is ___ in. The width of the prism is ____ in. The height of the prism is ___ in. The volume of the prism is ___ in.3.

15 4 5 300

Amelie bought a box of cereal with a length of 8 inches, a width of 4 inches, and a height of 12 inches. To determine the actual volume of cereal in the box, she opened the bag containing the cereal that came inside the box and poured it into the box. The cereal filled half of the box. What volume of cereal was in the bag? 12 in3 48 in3 192 in3 384 in3

192 in3

Which expressions show how to calculate the volume of this prism? Check all that apply. 2(12 + 21 + 28) 3(4) + 7 3(7)(4) 4(7)(3) 12(7) 21(28)

3(7)(4) 4(7)(3) 12(7)

Lloyd has a fish tank that is 8 inches high, 14 inches long, and 6 inches wide. If he fills the tank halfway with water, how many cubic inches of water are in the tank? 336 in.3 672 in.3 1,008 in.3 1,344 in.3

336 in.3

The highlighted bottom layer of the prism has a volume of 12 units3. What is the volume of the prism? ____ units3

36

What is the volume of the right rectangular prism? 23mm3 46mm3 432mm3 864mm3

432mm3

Alison made a three-layer gelatin dessert that was 15 cm long by 10 cm wide. The heights of the layers were 3 cm, 2 cm, and 1 cm. What is the total volume? The volume of the bottom layer is ___cm3. The volume of the middle layer is ___cm3. The volume of the top layer is___ cm3. The total volume is ___ cm3.

450 300 150 900

Salvatore began finding the volume of the box. His work is shown below. B=10(9)=90mm2 Using Salvatore's work as a starting point, what is the volume of the box? 90 mm3 95 mm3 190 mm3 450 mm3

450 mm3

What is the volume of the right rectangular prism, in cubic inches?

48 cubic inches

The length of the prism is __ m. The width of the prism is __ m. The height of the prism is __ m. unit cubes fill the prism. The volume of the prism is __ m3

5 1 6 30 30

Which is the correct calculation for the volume of the prism? 6 + 4 + 5 = 15 units3 6(4) + 5 = 29 units3 6(4) = 24 units3 6(4)(5) = 120 units3

6(4)(5) = 120 units3

Which is the correct calculation for the volume of the prism? 6 + 7 + 4 = 17 units3 6(4) + 7 = 31 units3 6(4) = 24 units3 6(7)(4) = 168 units3

6(7)(4) = 168 units3

Ivan wants to ship a box that is 6 in. tall, 4 in. wide, and 5 in. long to his cousin, and used the calculation below. What was his error, and what is the correct volume? V = lwh V = 5 x 4 x 6 = 20 x 6 = 26 in.3

Sample response: He added instead of multiplying 20 and 6. The correct answer is 120 cubic inches.

Volume of a prism

The volume of a prism is the product of the volume of one layer and the number of layers. Formula - V= lwh