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
Accepted Solution
A:
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