#### Question

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

#### Solution 1

Given that

A cone and a hemisphere have equal bases and volumes

`V_"cone" = V _"hemisphere"`

⇒ `1/3πr^2h=2/3πr^3`

⇒`r^2h=2r^3`

⇒`h=2r`

⇒`h:r -2r:r-2:1`

#### Solution 2

Given that

Volume of thee cone = Volume of the hemisphere

⇒`1/3πr^2h=2/3πr^3`

⇒`r^2h=2r^3`

⇒`h=2R`

⇒`h/r=1/1×2=2/1`

∴ Ratio of the their height is 2 :1

Is there an error in this question or solution?

#### APPEARS IN

Solution A Cone and a Hemisphere Have Equal Bases and Equal Volumes. Find the Ratio of Their Heights. Concept: Volume of a Sphere.