The radius of a cylinder is 8 cm and its height is 10 cm. If cones of radius 3 cm each and 4 cm deep are carved out from both ends of the cylinder, find the new surface area of the remaining solid?
1. 300π cm2
2. 302π cm2
3. 289π cm2
4. 298π cm2
1. 300π cm2
2. 302π cm2
3. 289π cm2
4. 298π cm2
Correct Answer – Option 1 : 300π cm2
Given:
Radius of a cylinder(R) = 8 cm
Height of cylinder = 10 cm
Radius of cone(r) = 3 cm
Height of cone = 4 cm
Concept:
The surface area of the remaining solid will be the sum of curved surface area of the cylinder, curved surface area of the cones, and the remaining area of the two circular faces of the cylinder.
Formula used:
Curved Surface area cylinder = 2πrh
Curved Surface area Cone = πrl
Slant height of cone = √(r2 + h2)
Surface area of remaining circular face of cylinder = π(R2 – r2)
Where ‘R’ is outer radius
And ‘r’ is inner radius
Calculation:
Curved surface area of cylinder = 2πRh
= 2 × π × 8 × 10
= 160π cm2 ——(1)
Slant height of cone = √[(3)2 + (4)2]
= √(25)
= 5cm
∴ CSA of cone on both faces = 2πrl
= 2 × 5 × 3 × π
= 30π cm2 ——(2)
Surface area of both faces of cylinder = 2π(R2 – r2)
= 2π[(8)2 – (3)2]
= 2π(64 – 9)
= 2π × 55
= 110π cm2 ——(3)
Adding (1), (2) and (3);
Surface area of total solid = (Curved surface area of cylinder) + (CSA of cone on both faces) + Surface area of both circular faces of cylinder)
= 160π cm2 + 30π cm2 + 110π cm2
= 300π cm2