Question

1.) A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone? A.) 2cm B.) 3cm C.) 4cm D.) 5cm

2.) A cylinder with a radius of 1cm and a height of 21cm has the same volume as a cone with a height of 7cm. What is the radius of the cone? A.) 3cm B.) 5cm C.) 7cm D.) 9cm

Answer 1

Part A)
we know that
[volume sphere]=(4/3)*pi*r³------> (4/3)*pi*3³--------> 113.04 cm³
[volume cone]=113.04=pi*r²*h/3------> h=[V*3]/[pi*r²]
r=6 cm
h=[V*3]/[pi*r²]---------> [113.04*3]/[pi*6²]---------> 3
h=3 cm

the answer part A) is h=3 cm

Part B)
[volume cylinder]=pi*r² *h---------> pi*1²*21------> 65.94 cm³
[volume cone]=65.94 cm³=pi*r²*h/3
h=7 cm
r=√[(V*3)/(pi*h)]---------> √[(65.94*3)/(pi*7)]---------> 3 cm

the answer Part B) is r=3 cm