Students can use the **Spectrum Math Grade 8 Answer Key** **Chapter 5 Lesson 5.13 Problem-Solving with Volume**Ā as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 5 Lesson 5.13 Problem-Solving with Volume Answers Key

**Solve each problem. Use 3.14 for Ļ. Round answers to the nearest hundredth.**

Question 1.

Jermaine has a mailing cylinder for posters that measures 18 inches long and 6 inches in diameter. What volume can it hold?

The cylinder can hold ___________________ cubic inches.

Answer: The cylinder can hold 508.68 cubic inches.

Jermaine has a mailing cylinder for posters that measures 18 inches long and 6 inches in diameter.

Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, Ļr^{2}, so volume can be found using the formula: V = Ļr^{2}h

The volume is expressed in cubic units, or units^{3}.

The given values are d = 6 in. so, r = d/2 = 6/2 = 3 in. and h = 18 in.

Use 3.14 for Ļ.

So, V = Ļr^{2}h V = Ļ(3^{2} Ć 18) V = 508.68 in^{3
}Therefore, The cylinder can hold 508.68 cubic inches.

Question 2.

An oatmeal container is a cylinder measuring 16 centimeters in diameter and 32 centimeters tall. How much oatmeal can the container hold?

The container can hold ___________________ cubic centimeters of oatmeal.

Answer:Ā The container can hold 6430.72 cubic centimeters of oatmeal.

An oatmeal container is a cylinder measuring 16 centimeters in diameter and 32 centimeters tall.

Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, Ļr^{2}, so volume can be found using the formula: V = Ļr^{2}h

The volume is expressed in cubic units, or units^{3}.

The given values are d = 16 cms so, r = d/2 = 16/2 =8 cms and h = 32 cms

Use 3.14 for Ļ.

So, V = Ļr^{2}h V = Ļ(8^{2} Ć 32) V = 6430.72 cms^{3
}Therefore, The container can hold 6430.72 cubic centimeters of oatmeal.

Question 3.

Trina is using 2 glasses in an experiment. Glass A measures 8 centimeters in diameter and 18 centimeters tall. Glass B measures 10 centimeters in diameter and 13 centimeters tall. Which one can hold more liquid? How much more?

Glass ____________________ can hold ____________________ more cubic centimeters of liquid.

Answer: Glass B can hold A more cubic centimeters of liquid.

Trina is using 2 glasses in an experiment. Glass A measures 8 centimeters in diameter and 18 centimeters tall. Glass B measures 10 centimeters in diameter and 13 centimeters tall.

Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, Ļr^{2}, so volume can be found using the formula: V = Ļr^{2}h

The volume is expressed in cubic units, or units^{3}.

Volume of Glass A:

The given values are d = 8 cms so, r = d/2 = 8/2 =4 cms and h = 18 cms

Use 3.14 for Ļ.

So, V = Ļr^{2}h V = Ļ(4^{2} Ć 18) V = 904.32 cms^{3
}Volume of Glass B:

The given values are d = 10 cms so, r = d/2 = 10/2 =5 cms and h = 13 cms

Use 3.14 for Ļ.

So, V = Ļr^{2}h V = Ļ(5^{2} Ć 13) V = 1020.5 cms^{3
}Volume of glass B is greater than volume of glass A

Therefore, Glass B can hold A more cubic centimeters of liquid.

Question 4.

Paul completely filled a glass with water. The glass was 10 centimeters Ā”n diameter and 17 centimeters tall. He drank the water. What volume of water did he drink?

Paul drank __________________ cubic centimeters of water.

Answer:Ā Paul drank 1334.5 cubic centimeters of water.

Paul completely filled a glass with water. The glass was 10 centimeters Ā”n diameter and 17 centimeters tall. He drank the water.

Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, Ļr^{2}, so volume can be found using the formula: V = Ļr^{2}h

The volume is expressed in cubic units, or units^{3}.

The given values are d = 10 cms so, r = d/2 = 10/2 = 5 cms and h = 17 cms

Use 3.14 for Ļ.

So, V = Ļr^{2}h V = Ļ(5^{2} Ć 17) V = 1334.5 cms^{3
}Therefore, Paul drank 1334.5 cubic centimeters of water.

Question 5.

An ice-cream cone has a height of 6 inches and a diameter of 3 inches. How much ice cream can this cone hold?

The cone can hold ___________________ cubic inches of ice cream.

Answer:Ā The cone can hold 14.13 cubic inches of ice cream.

An ice-cream cone has a height of 6 inches and a diameter of 3 inches.

Volume is the amount of space a three-dimensional figure occupies. The volume of a cone is calculated as \(\frac{1}{3}\)base Ć height.

This is because a cone occupies \(\frac{1}{3}\) of the volume of a cylinder of the same height. Base is the area of the circle, Ļr^{2}.

radius = 3 / 2= 3 / 2 = 1.5 in.

height = 6 in.

V = \(\frac{1}{3}\)Ļr^{2}h =Ā \(\frac{1}{3}\)Ļ1.5^{2} 6 = 14.13 in.^{3
}Therefore, The cone can hold 14.13 cubic inches of ice cream.

Question 6.

A beach ball that is 10 inches in diameter must be inflated. How much air will it take to fill the ball?

It will take _____ cubic inches of air to fill the ball.

Answer: It will take 523.33 cubic inches of air to fill the ball.

A beach ball that is 10 inches in diameter must be inflated.

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)Ļr^{3}.

\(\frac{4}{3}\)Ļr^{3} Volume is given in cubic units or units^{3}.

Given, d = 10 in.

The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.

r = \(\frac{1}{2}\)d = \(\frac{1}{2}\)(10) = 5

V = \(\frac{4}{3}\)Ļ(5)^{3} =Ā 523.33 in^{3
}Therefore, It will take 523.33 cubic inches of air to fill the ball.