from a solid cylinder of height 28cm and radius 12cm a conical cavity of height 16cm and radius 12cm - Physics - Units and Measurements

Question

from a solid cylinder of height 28cm and radius 12cm a conical
cavity of height 16cm and radius 12cm is drilled out find the
volume and total surface area of the remaining solid?

Aakash Sharma · Accepted Answer

Volume of remaining solid = Volume of cylinder – Volume of cone

$= π (12 cm)^{2} (28 cm) - \frac{1}{3} π (12 cm)^{2} (16 cm) = 144 π (28 + \frac{16}{3}) {cm}^{3} = \frac{14400}{3} π {cm}^{3} = 4800 π {cm}^{3}$

and T.S. A of remaining solid = C.S.A. of cylinder + C.S.A of cone + Area of base

= 2 π (12 cm) (28 cm) + π (12 cm) (20 cm) + π (12 cm)²

$(∵ slant height = \sqrt{(12 cm)^{2} + (16 cm)^{2}} = \sqrt{400 {cm}^{2}} =20 cm)$

= 12 π [56 + 20 + 12] cm²

= 12 × 88 π cm² = 1056 π cm²

3

from a solid cylinder of height 28cm and radius 12cm. a conical cavity of height 16cm and radius 12cm is drilled out . find the volume and total surface area of the remaining solid?