1 simple question...and a hard one :D?

Question

Find the volume of a sphere with radius 3 cm. Leave answers in terms of pi.

For an answer I got 113 cm. Do they want me to put a pi symbol after 113?

and for the hard question:

The volumes of two similar pyramids are 27 and 64. If the smaller has lateral area of 18, find the lateral area of the larger. (Hint: Apply thereom 12-11.)

HELP!!!

Answer 1

The volume, V, of a sphere is given by the formula:

V = four thirds pi r cubed, V=4/3pir^3 so, if r = 3, then

V = 4/3 pi 3*3*3

V = 36 pi.

If two bodies are similar, then:

The volumes of the two bodies are in the ratio of the cubes of

the ratio of their linear lengths.

The areas are in the ratio of the squares of their linear

lengths

The ratio of their volumes is 27 to 64, so the ratio of their

linear lengths will be in the ratio cube rt27: cube rt 64, that is

3:4, and the ratio of areas will be in the ratio 3^2:4^2, that is

9:16

Let the area of the larger pyramid be A, so,

9/16 = 18/A, so,

9A = 18*16, so,

A = 32. Hope this helps, Twiggy.

Answer 2

V=4/3pir^3=4/3*27*pi= 36picm^3
The sides are in the ratio (64/27)^1/3= 4/3 and the areas are in ratio(4/3)^2
so the area is 16/9*18 =32 cm^2