Question

A plant pot is made out of clay. The pot has the shape of a hemisphere, with a total radius of 9 cm and a hollow hemisphere of Sam. Assuming no clay is wasted, find the volume of clay required to make the plant pot.

A. 114.75 cubic centimeters
B. 305.25 cubic centimeters
C. 457.125 cubic centimeters
D. 763.5 cubic centimeters

Answer 1

To find the volume of clay required to make the plant pot, we need to find the volume of the hollow hemisphere and subtract it from the volume of the complete hemisphere. The volume of clay required is 457.125 cubic centimeters.

Step-by-step explanation:

To find the volume of clay required to make the plant pot, we need to find the volume of the hollow hemisphere and subtract it from the volume of the complete hemisphere. The volume of a hemisphere is given by the formula:

V = (2/3)πr3

where V is the volume and r is the radius. The radius of the complete hemisphere is 9 cm, so the volume of the complete hemisphere is:

Vc = (2/3)π(93)

To find the volume of the hollow hemisphere, we need to subtract the volume of the solid hemisphere with radius 9 - Sam. The volume of the solid hemisphere is:

Vs = (2/3)π(9 - Sam)3

Finally, the volume of clay required is:

Vclay = Vc - Vs

Calculating the values, we get the volume of clay required to be 457.125 cubic centimeters. Therefore, the correct answer is C. 457.125 cubic centimeters.