Question

cylinders
one of the main methods that a fruit company uses to distribute its fruit is in cans. because the fruit company sells its canned fruit in different forms, it distributes its fruit in cans of different sizes.
label each can with the measurements described. use those measurements to determine the volume. use 3.14 as an approximation for ( pi ). round to the nearest hundredth, if necessary.

1. a can of pineapple pieces has a radius of 9 cm and a height of 4 cm. what is the volume of the can of pineapple pieces?

formula:
substitute in numbers: ( v = pi (quad)(quad) )
simplified in terms of pi (( pi )):
simplified answer w/ units:

1. a small can of orange juice has a diameter of 3 inches and a height of 5 inches. what is the volume of the can of orange juice?

formula:
substitute in numbers: ( v = pi (quad)(quad) )
simplified in terms of pi (( pi )):
simplified answer w/ units:

Explanation:

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Problem 1: Pineapple Can

Step1: Recall cylinder volume formula

The base area $B$ of a cylinder is $\pi r^2$, so $V = \pi r^2 h$.

Step2: Substitute given values

$r=9$ cm, $h=4$ cm:
$V = \pi(9^2)(4)$

Step3: Simplify in terms of $\pi$

$V = \pi(81)(4) = 324\pi$

Step4: Calculate numerical value

Use $\pi=3.14$:
$V = 324 \times 3.14 = 1017.36$

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Problem 2: Orange Juice Can

Step1: Find radius from diameter

Radius $r = \frac{\text{diameter}}{2} = \frac{3}{2} = 1.5$ inches

Step2: Substitute into volume formula

$r=1.5$ in, $h=5$ in:
$V = \pi(1.5^2)(5)$

Step3: Simplify in terms of $\pi$

$V = \pi(2.25)(5) = 11.25\pi$

Step4: Calculate numerical value

Use $\pi=3.14$:
$V = 11.25 \times 3.14 = 35.325 \approx 35.33$

Answer:

1. Pineapple Can:

• Formula: $V = Bh = \pi r^2 h$
• Substitute in numbers: $V = \pi(9^2)(4)$
• Simplified in Terms of Pi ($\pi$): $324\pi$
• Simplified Answer w/ units: $1017.36$ cubic centimeters

1. Orange Juice Can:

• Formula: $V = Bh = \pi r^2 h$
• Substitute in numbers: $V = \pi(1.5^2)(5)$
• Simplified in Terms of Pi ($\pi$): $11.25\pi$
• Simplified Answer w/ units: $35.33$ cubic inches