Question #90473

2 Answers
Apr 18, 2017

13500cm^3

Explanation:

pi=3 " for this question"

"surface area of a sphere "=4pir^2

:.4pir^2=2700

4xxcancel(3)xxr^2=cancel(2700)^900

r^2=900/4

r=sqrt(900/4)=30/2=15 cm

"volume of sphere "=4/3pir^3

V=4/cancel(3)xxcancel(3)xx15^3

V=4xx15xx15xx15=13500cm^3

Apr 18, 2017

13500cm^3

Explanation:

Surface are of a sphere ( the globe in this case) is given by:-
color(red)(S = 4*pi*r^2) where r is radius of sphere.

The volume of a sphere is given by:-
color(red)(V = 4/3*pi*r^3) where r is the radius of sphere.

Given that pi = 3.

Surface area is 2700 cm^2.
therefore 4*pi*r^2 = 2700
=> 4*3*r^2 = 2700
=>r^2 = 2700/(3*4) = 900/4
=> r = sqrt(900/4) = 30/2 = 15cm.

Method 1.
Now volume is 4/3*pi*r^3
therefore V = 4/3*3*15^3 = 4*3375 = 13500cm^3

Method 2.
S = 4*pi*r^2 ------------------(1.)
V = 4/3*pi*r^3 ------------------(2.)

Dividing equations (1.) & (2.)
S/V = (4*cancelpi*r^2)/(4/3*cancelpi*r^3) = 3/r

=> S/V = 3/r

=> V = (S*r)/3 = (2700*15)/3 = 13500cm^3