Solve the problem.
-A company applies a clear glaze finish on the outside of the ceramic bowls it produces. The bowl corresponds to the bottom half of a sphere which is created by rotating the circle $x ^ { 2 } + y ^ { 2 } = 36$ around the $x$-axis. The finish is to be $0.2 \mathrm {~cm}$ thick, and the company wants to create 3000 bowls. Use the fact that $1 \mathrm {~L} = 1000 \mathrm {~cm} ^ { 3 }$ to calculate how many liters of finish are required. Assume that all specifications for the bowl are in $\mathrm { cm }$.
A) 2.26 L of finish
B) 226.19 L of finish
C) 67.86 L of finish
D) 135.72 L of finish

Question

Quizplus · Accepted Answer

The volume of the glaze needed for one bowl is the difference between the volumes of the outer and inner spheres. The radius of the inner sphere (the bowl) is 6 cm, so the radius of the outer sphere (with the glaze) is 6.2 cm. The volume of a sphere is $V = \frac{4}{3}\pi r^3$. Thus, the volume of glaze for one bowl is $\frac{4}{3}\pi (6.2)^3 - \frac{4}{3}\pi (6)^3$. For 3000 bowls, multiply this volume by 3000 and convert to liters ($1 L = 1000 cm^3$). This calculation results in approximately 135.72 liters of finish required.

Solve the Problem x2+y2=36x ^ { 2 } + y ^ { 2 } = 36x2+y2=36

Solve the Problem $x ^ { 2 } + y ^ { 2 } = 36$