Question

Jessica has a barrel to fill with water. The barrel is 24 inches high with a radius of 12 inches. She is using a cup to fill the the barrel. The cup has a height of 6 inches and diameter of 4 inches. How many full cups will she need in order to fill the barrel?

Answer 1

SOLUTION.

The barrel and the cub are both cylinders. To find how many cups that will fill the barrel, we find the volumes of both the cup and the barrel and divide that of the barrel by the cup

Volume of a cylinder is given as

`\begin{gathered} \text{Volume = }\pi r^2h,\text{ r is radius and h is height of the cylinder } \\ radius\text{ of the barrel = }12,\text{ height = 24} \\ \text{Volume of barrel = }\pi r^2h \\ \text{Volume of barrel = 3.14}*12^2*24 \\ \text{Volume of barrel = }10851.84inch^3 \end{gathered}`

Volume of the cub becomes

`\begin{gathered} \text{radius of cup = }(4)/(2)=2 \\ \text{Volume of barrel = }\pi r^2h \\ \text{Volume of cup = }3.14*2^2*6 \\ \text{Volume of cup = }75.36inches^3 \end{gathered}`

Number of cups become

`(10851.84)/(75.36)\text{ = 144 cups }`