Question

From a solid cylinder whose height is 8cm, and radius 6 cm,a conical cavity of height 8cm and of base radius 6cm,a conical cavity of height 8cmand of base radius 6 cm, is hollowed out.Find the volume of the remaining solid corect to two places of decimals.Also find thee total surface area of the remaining solid

Answer 1

Hiiii friend,


Height of cylinder = 8 cm


Radius of cylinder = 6 cm


Volume of cylinder = πR²H



=> 22/7 × 6 × 6 × 8


=> 22 × 6 × 6 × 8/7


=>6336/7

=> 905.14 cm²

Height of Cone = 8 cm


Radius of cone = 6 cm


Slant Height (L) = ✓(H)²+(R)² => ✓(8)²+(6)²


Slant Height (L) = ✓64+36 = ✓100 = 10 cm


Volume of cone = 1/3πR²H



=> 1/3 × 22/7 × 6 × 6 × 8


=> 22 × 6 × 6 × 8/21


=> 6336/21



=>301.71 cm².


Volume of remaining solid = Volume of cylinder- Volume of cone


=> πR²H - 1/3πR²H


=> 2/3 πR²H


=> 2/3 × 22/7 × 6 × 6 × 8


=> 2 × 22 × 6 × 6 × 8/21


=> 12672/21


=> 603.42 cm².



TSA of remaining solid = CSA of cylinder +CSA of cone + Area of upper circular face of cone



=> 2πRH + πRL + πR²


=> πR(2H+L+R)


=> 22/7 × 6 ( 2 × 8 + 10 + 6)


=> 132/7 ( 16 + 16)


=> 132/7 × 32


=> 132 × 32/7


=> 4224/7


=> 603.42 cm².



HOPE IT WILL HELP YOU...... :-)

Answer 2

Volume of remaining solid is 602.88 cubic cm.

Total surface area of remaining solid is 602. 88 cubic cm.