Assertion (A) : The maximum volume of a cone that can be carved out of a solid hemisphere of radius r is $\dfrac{1}{3}$ r³.
Reason (R) : For a cone of radius r and height h, volume is given by $\dfrac{2}{3}$ πr²h.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false

Question

Assertion (A) : The maximum volume of a cone that can be carved out of a solid hemisphere of radius r is $\dfrac{1}{3}$ r³.

Reason (R) : For a cone of radius r and height h, volume is given by $\dfrac{2}{3}$ πr²h.

KnowledgeBoat · Accepted Answer

The maximum height and radius of cone, inside a hemisphere of radius r cm can be r cm.

Volume of cone = $\dfrac{1}{3}$ πr²h

$= \dfrac{1}{3} π\text{r}^2\text{r} \\[1em] = \dfrac{1}{3} π\text{r}^3 \\[1em]$

∴ Assertion (A) is false.

For a cone of radius r and height h.

Volume of cone = $\dfrac{1}{3}$ πr²h

∴ Reason (R) is false.

Hence, option 4 is the correct option.

Mathematics