Question

1. the silo at a farm is shaped like a cylinder. with a radius of 8 feet and a volume of 3217 ft³, what is the height of the silo? round to the nearest tenth.
2. matthew makes a cardboard container shaped like a cone with a height of 6 cm and the area of the base is 50.3 cm². what is the volume of the cardboard container matthew created? round to the nearest tenth.
3. three tennis balls are placed in a cylindrical tube for sale. use the diagram below to determine the volume of one tennis ball.

(diagram: a cylindrical tube with three tennis balls inside, height h = 20.1 cm)

1. at an office, employees use small cone - shaped cups when getting water from a water cooler. each cup has a height of 10 centimeters and a diameter of 6 centimeters. roger filled his cone - shaped cups and has a total volume of 565.5 cubic centimeters, how many cups of water did he fill?

Explanation:

Problem 3

Step1: Recall cylinder volume formula

The volume \( V \) of a cylinder is given by \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. We need to solve for \( h \), so rearrange the formula: \( h=\frac{V}{\pi r^2} \).

Step2: Substitute given values

Given \( V = 3217\space ft^3 \) and \( r = 8\space ft \). Substitute into the formula: \( h=\frac{3217}{\pi\times8^2} \).

Step3: Calculate denominator

First, calculate \( 8^2 = 64 \), then \( \pi\times64\approx 201.06 \).

Step4: Solve for h

Now, \( h=\frac{3217}{201.06}\approx16.0 \) (rounded to the nearest tenth).

Step1: Recall cone volume formula

The volume \( V \) of a cone is given by \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height.

Step2: Substitute given values

Given \( B = 50.3\space cm^2 \) and \( h = 6\space cm \). Substitute into the formula: \( V=\frac{1}{3}\times50.3\times6 \).

Step3: Calculate the volume

First, \( 50.3\times6 = 301.8 \), then \( \frac{1}{3}\times301.8 = 100.6 \).

Step1: Determine radius and height of one tennis ball

From the diagram, the height of the cylinder (which holds three tennis balls) is \( h = 20.1\space cm \). So the diameter of one tennis ball (which is a sphere) is \( \frac{20.1}{3}=6.7\space cm \), so the radius \( r=\frac{6.7}{2}=3.35\space cm \).

Step2: Recall sphere volume formula

The volume \( V \) of a sphere is \( V=\frac{4}{3}\pi r^3 \).

Step3: Substitute radius into formula

Substitute \( r = 3.35\space cm \) into the formula: \( V=\frac{4}{3}\pi\times(3.35)^3 \).

Step4: Calculate \( (3.35)^3 \)

\( 3.35^3=3.35\times3.35\times3.35\approx 37.595 \).

Step5: Calculate volume

Then \( V=\frac{4}{3}\pi\times37.595\approx\frac{4}{3}\times3.14\times37.595\approx 157.6\space cm^3 \) (rounded appropriately).

Answer:

The height of the silo is approximately \( 16.0 \) feet.

Problem 4