Question

There is a solid ball that weighs 1000g. The radius of the ball is 5 cm.

1. What is the density of the ball? (π=3)    in kg/m³    (no unit needed in the answer )  

π

2. If you cut a smaller ball, which has a radius of 1 cm, from this big ball. What is the mass left? ( $\pi$ π=3)    in kg    (no unit needed in the answer )  

3. What is the volume ratio of those two balls? (small : big)  

Answer 1

1) We know that density d=M/V ....1

here M=1000g =1.0 kg , V=4$\prod$R³/3 R=5 cm =0.05 m ,$\prod$=3 , so V=4$\prod$(0.05³)/3 =5*10^-4 m³

d=1/5*10^-4

d=2000 kg/m³

2) volume of the small ball (R=1cm=0.01 m) V_s=4$\prod$(0.01³)/3 =*10^-6 m³

mass of the ball m=dV =2000*4*10^-6

m=8000 *10^-6

m=8*10^-3 kg

left mass =1-0.008=0.992 kg answer

3)

V_s/V=4.*10^-6/5*10^-4

=0.8*10^-2

=0.008 answer