SOLUTION: A sphere circumscribes a right circular cylinder of altitude 9 cm and diameter 7 cm, find the ratio of their (a) volumes (b) total surfaces areas.

Question 1189062: A sphere circumscribes a right circular cylinder of altitude 9 cm and diameter 7 cm, find the ratio of their (a) volumes (b) total surfaces areas.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Draw this
Cylinder has height 9 cm and radius 3.5 cm and therefore volume of πr^2h=110.25π cm^3
the sphere's radius goes from the center to one side of the cylinder at the edge. In that triangle, the hypotenuse is the radius of the sphere, one side is the radius of the cylinder, 3.5 cm, and the other side is half the elevation, or 4.5 cm Therefore, the radius of the sphere is sqrt (3.5^2+4.5^2)=5.701 cm, and the volume is (4/3)π*5.701^3=247.04π cm^3
This makes the c/s ratio 110.25π/247.05π=0.4463
-
area of the cylinder is 2πrh+2πr^2h=7*9*π+220.5π=283.5π
area of sphere is 4πr^2=4*5.701^2*π=130.01π cm^2
That ratio of c/s=2.181
RELATED QUESTIONS
find the surface area of a right circular cylinder that 6 cm. in diameter and is 12 cm.... (answered by mananth)

The lateral surface of a right circular cylinder is 330π sq. cm.. If its altitude... (answered by macston)

A cylinder and a cone have base radii 5 cm and 3 cm respectively and their respective... (answered by sarcasticpie,MathTherapy)

A large and a small sphere have volumes 135 cm cubed and 40 cubed. Find the ratio of... (answered by Alan3354)

A sphere circumscribes a cube of side 4cm. a) What is the radius of the sphere? b) Find (answered by math_helper)

a right circular cone has an altitude of 25 cm and a base diameter of 20cm rest on the... (answered by addingup)

A sphere is just inclosed inside the right circular cylinder. If the volume of the gap... (answered by ankor@dixie-net.com)

17. Find the volume of the largest right circular cylinder of altitude 8 in. that can be... (answered by CPhill,greenestamps)

Find the dimensions and volume of the right circular cylinder of maximum volume inscribed (answered by josgarithmetic)