Answer:
101.0 in³ = 1.656 liters
Step-by-step explanation:
Formulas
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
[tex]\textsf{Diameter of a circle}=2r \quad\textsf{(where r is the radius)}[/tex]
Given dimensions of cylinder:
- diameter = 4 in
- height = 12 in
First, calculate the radius by halving the diameter:
[tex]\implies \textsf{Radius }(r)=4 \div 2=2\: \sf inches[/tex]
Substitute the given values into the formula to find the volume of the cup:
[tex]\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}[/tex]
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%:
[tex]\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}[/tex]
Liquid is usually measured in liters.
To convert cubic inches to liters, multiply by 0.016387064:
[tex]\implies \sf 101.0336197...in^3 \times 0.016387064 = 1.656 \: liters\:(3\:dp)[/tex]
