Question

A cylindrical cup with a base diameter of 4 inches and a height of 12 inches is filled with orange juice that occupies 67% of the cup. What is the volume of the orange juice in the cup?

Answer 1

• radius=r=4/2=2in

Volume

• πr²h
• π(2)²(12)
• 48π
• 150.7in³

Volume of orange juice

• 67% of 150.7
• 0.67(150.7)
• 100.969in³

Answer 2

101.0 in³ = 1.656 liters

Explanation:

Formulas

`\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}`

`\textsf{Diameter of a circle}=2r \quad\textsf{(where r is the radius)}`

Given dimensions of cylinder:

• diameter = 4 in
• height = 12 in

First, calculate the radius by halving the diameter:

`\implies \textsf{Radius }(r)=4 / 2=2\: \sf inches`

Substitute the given values into the formula to find the volume of the cup:

`\begin{aligned}\textsf{Volume of a cylinder} & = \pi r^2h\\ \implies \textsf{Volume of the cup} & = \pi \cdot (2)^2 \cdot 12\\& = \pi \cdot 4 \cdot 12\\& = 48\pi \sf \:\:in^3 \end{aligned}`

The cup is filled with orange juice that occupies 67% of the cup. To find the volume of orange juice in the cup, multiply the found volume of the cup by 67%:

`\begin{aligned}\implies\textsf{Volume of orange juice} & = 67\% \textsf{ of }48 \pi \\\\& = (67)/(100) \cdot 48 \pi \\\\& = (3216)/(100) \pi \\\\& = 101.0336197...\\\\& = 101.0\:\: \sf in^3\:(nearest\:tenth) \end{aligned}`

Liquid is usually measured in liters.

To convert cubic inches to liters, multiply by 0.016387064:

`\implies \sf 101.0336197...in^3 * 0.016387064 = 1.656 \: liters\:(3\:dp)`