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Question
From a solid cylinder whose height is 15 cm and diameter 16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Use π = 3.14)
Solution
We have,
Height of the cylinder = Height of the cone = h = 15 cm and
Radius of thecylinder = Radius of the cone `= r = 16/2 = 8 "cm" `
Also, the slant height of the cone, `l =sqrt("h"^2 + "r"^2)`
`=sqrt(15^2 + 8^2)`
`=sqrt(225+64)`
`=sqrt(289)`
= 17 cm,
Now,
Then total surface area of the remaining solid = CSA of the cone + CSA of the cone + Area of the base
=πrl+ 2πrh + πr2
= πr (l + 2h + r)
= 3.14 × 8× (17 + 2 × 15 + 8)
= 3.1× 8 × 55
= 1381.6 cm2
So, the total surface area of the remaining solid is 1381.6 cm2.
Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.
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