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:
Option B.
Step-by-step explanation:
Volume of cone is
\(V_1=\dfrac{1}{3}\pi r^2h\)
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.
\(V_1=\dfrac{1}{3}\pi (1.5)^2(6)=14.137167\approx 14.14\)
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.