Question

From a solid cylinder of height 12 cm and radius 5 cm, a conical cavity of same height and radius is hollowed out. Find the total surface area of the remaining solid.

Answer 1

Answer:

660 cm²

Step-by-step explanation:

Given---> From solid cylinder of height 12 cm and base radius of 5cm , a conical cavity of same height and same radius is hollowed out.

To find----> Total surface area of the remaining solid.

Solution---> Total surface area of remaining solid is the sum of curved surface area of cylinder which is outer surface of remaining solid , curved surface area of cone which is inner surface area of remaining solid and area of circular end which is at top .

Now first , we find , slant height of conical cavity,

ATQ,

Height of Conical cavity = height of cylinder

=> Height of conical cavity = 12 cm

Radius of conical cavity = Radius of base of cylinder

=> Radius of conical cavity = 5cm

Let slant height of conical cavity be l , then,

l² = r² + h²

=> l² = 5² + 12²

=> l² = 25 + 144

=> l² = 169

=> l = √169

=> l = 13 cm

Curved surface area of conical cavity = πrl

= π × 5 × 13

= 65 π cm²

Curved surface area of cylinder = 2 π r h

= 2 × π × 5 × 12

= 120 π cm²

Area of circular end at the top = π r²

= π ( 5 )²

= 25 π cm²

Now area of remaining solid

= CSA of cylinder + CSA of conical cavity + area of circular top

= 120 π + 65 π + 25 π

= 210 π

= 210 × ( 22 / 7 )

= 210 × 22 / 7

= 30 × 22

= 660 cm²

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Answer 2

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