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

Answer:

101.0 in³ = 1.656 liters

Step-by-step 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:

$\implies \textsf{Radius }(r)=4 \div 2=2\: \sf inches$

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%:

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

Liquid is usually measured in liters.  

To convert cubic inches to liters, multiply by 0.016387064:

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