Question

Look at the cups shown below (please note that images are not drawn to scale): A cone is shown with width 3 inches and height 6 inches, and a cylinder is shown with width 3 inches and height 5 inches How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth. 18.8 cubic inches 21.2 cubic inches 28.2 cubic inches 49.5 cubic inches

Answer 1

the answer is 21.2 cubic inches

Answer 2

Option B.

Explanation:

Volume of cone is

`V_1=(1)/(3)\pi r^2h`

where, r is radius and h is height of the cone.

Cup A is a cone with width 3 inches and height 6 inches. It means radius is 1.5 inches.

Substitute r=1.5 and h=6 in the above formula.

`V_1=(1)/(3)\pi (1.5)^2(6)=14.137167\approx 14.14`

Volume of cylinder is

`V_2=\pi r^2h`

where, r is radius and h is height of the cylinder.

Cup B is a cylinder with width 3 inches and height 5 inches.

Substitute r=1.5 and h=5 in the above formula.

`V_2=\pi (1.5)^2(5)=35.342917\approx 35.34`

Difference between their volumes is

`35.34-14.14=21.2`

It means cup B can hold 21.2 cubic inches more than cup A when both are completely full.

Therefore, the correct option is B.