MATH SOLVE

10 months ago

Q:
# 1. A soup company uses a cylindrical can for their soup with a radius of 4 cm. If the volume of the can is 240π cm3, what is the height of the can?Explain how you determined the answer.2.Consider a cylinder with radius 4 cm and a height of 12 cm.Describe how to calculate the volume of the given cylinder and what the volume means.3.A cracker company wants to make a rectangular box to hold their crackers.They want the height of the box to be 10 inches and the width to be 4 inches.Explain how to calculate the length the box needs to be in order for the volume of the box to be 200 cubic inches.

Accepted Solution

A:

First, its important that we review what types of shapes we have. In the first two problems, we have a cylinder. In the last problem, we have a rectangle. The formulas for volume of a cylinder and a rectangle are:

Cylinder

V = [tex] \pi r^2[/tex]

Rectangle

V = L x W x H

In the first problem, we have a cylinder and we are looking for the height. We know the volume (240), and we know the radius (4). We can use these values to fill in our formula, and then solve for the missing height. (This process is shown in the image).

In the second problem, we have a cylinder and we are looking for the volume. We know the radius (4), and we know the height (12). We can use these values to fill in our formula, and then solve for the volume. (This process is shown in the image).

In the third problem, we have a rectangle and we are looking for the length. We know the height (10), we know the width (4), and we know the volume (200). We can use these values to fill in our formula, and then solve for the length. (This process is shown in the image).

Cylinder

V = [tex] \pi r^2[/tex]

Rectangle

V = L x W x H

In the first problem, we have a cylinder and we are looking for the height. We know the volume (240), and we know the radius (4). We can use these values to fill in our formula, and then solve for the missing height. (This process is shown in the image).

In the second problem, we have a cylinder and we are looking for the volume. We know the radius (4), and we know the height (12). We can use these values to fill in our formula, and then solve for the volume. (This process is shown in the image).

In the third problem, we have a rectangle and we are looking for the length. We know the height (10), we know the width (4), and we know the volume (200). We can use these values to fill in our formula, and then solve for the length. (This process is shown in the image).