Spectrum Math Grade 8 Chapter 5 Lesson 13 Answer Key Problem-Solving with Volume

Students can use the Spectrum Math Grade 8 Answer Key Chapter 5 Lesson 5.13 Problem-Solving with Volume 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 π. 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, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are d = 6 in. so, r = d/2 = 6/2 = 3 in. and h = 18 in.
Use 3.14 for π.
So, V = πr²h V = π(3² × 18) V = 508.68 in³
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:  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, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are d = 16 cms so, r = d/2 = 16/2 =8 cms and h = 32 cms
Use 3.14 for π.
So, V = πr²h V = π(8² × 32) V = 6430.72 cms³
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, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
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 π.
So, V = πr²h V = π(4² × 18) V = 904.32 cms³
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 π.
So, V = πr²h V = π(5² × 13) V = 1020.5 cms³
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 ¡n diameter and 17 centimeters tall. He drank the water. What volume of water did he drink?
Paul drank __________________ cubic centimeters of water.
Answer:  Paul drank 1334.5 cubic centimeters of water.
Paul completely filled a glass with water. The glass was 10 centimeters ¡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, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are d = 10 cms so, r = d/2 = 10/2 = 5 cms and h = 17 cms
Use 3.14 for π.
So, V = πr²h V = π(5² × 17) V = 1334.5 cms³
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:  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 × 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, πr².
radius = 3 / 2= 3 / 2 = 1.5 in.
height = 6 in.
V = \(\frac{1}{3}\)πr²h =  \(\frac{1}{3}\)π1.5² 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 = \(\frac{4}{3}\)πr³.
\(\frac{4}{3}\)πr³ Volume is given in cubic units or units³.
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 = \(\frac{4}{3}\)π(5)³ =  523.33 in³
Therefore, It will take 523.33 cubic inches of air to fill the ball.