Question

"The volume of a cone V is equal to the product of one third of π and square of radius r of the base and the height h". Express this statement as a formula. Make r the subject formula. Find r, when V = 1232cm³, π = `(22)/(7)`, h = 24cm.

Answer 1

Volume of cone = V
Product of one third of π and square of radius r of the base and the height h = `(1)/(3)pi"r"^2"h"`

So, V = `(1)/(3)pi"r"^2"h"`

⇒ `(3"V")/(pi"h")` = r² 

⇒ r = `sqrt((3"V")/(pi"h")`

Substituting V = 1232cm³, π = `(22)/(7)`, h = 24cm

⇒ r = `sqrt((3 xx 1232)/(22/7 xx 24)`

= `sqrt(49)`
= 7cm.