Assertion (A): From a solid wooden cylinder of height 15 cm and diameter 14 cm, a hemispherical depression of same base diameter is carved out. The volume of remaining wood is $1591\dfrac{1}{3}$ cm³.

Reason (R): The volume of a cylinder of height h and radius r is πr²h and the volume of a hemisphere of radius r is $\dfrac{2}{3}$ πr³.

Given,

Height of cylinder,(H) = 15 cm

Diamter of cylinder, (D) = 14 cm

Radius of cylinder, r = $\dfrac{D}{2} = \dfrac{14}{2}$ = 7 cm

Radius of hemisphere, (r) = 7 cm

The volume of a cylinder is πr²h and the volume of a hemisphere is $\dfrac{2}{3}$ πr³.

So, reason (R) is true.

Volume of remaining wood = Volume of cylinder - Volume of hemisphere

$= πR^2H - \dfrac{2}{3}πr^3\\[1em] = \dfrac{22}{7} \times 7^2 \times 15 - \dfrac{2}{3}\times \dfrac{22}{7} \times 7^3\\[1em] = 22 \times 7 \times 15 - \dfrac{2}{3}\times 22 \times 7^2\\[1em] = 2310 - \dfrac{2156}{3}\\[1em] = \dfrac{6930 - 2156}{3}\\[1em] = \dfrac{4774}{3}\\[1em] = 1591\dfrac{1}{3}\\[1em]$

So, assertion (A) is true.

Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.