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 + πr^{2 }

= πr (l + 2h + r)

= 3.14 × 8× (17 + 2 × 15 + 8)

= 3.1× 8 × 55

= 1381.6 cm^{2}

So, the total surface area of the remaining solid is 1381.6 cm^{2}.

Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.