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 $\pi$ = 3.14)

Answer 1

We have,Height of the cylinder=Height of the cone

$\Rightarrow h=15cm$

And radius of the cylinder=Radius of the cone

$\Rightarrow r=\frac{16}{2}=8cm$

Also, the slant height of the cone,

$l=h^2+r^2={15}^2+8^2=225+64=289=17cm$

Now,The total surface area of the remaining solid=CSA of the cone+CSA of the cylinder

+Area of the base

$=\pi rl+2\pi rh+\pi r^2=\pi r[l+2h+r]$

$=3.14\times 8[17+2\times 15+8]$

$=3.14\times 8\times 55=1381.6c{m}^2$
So, the total surface area of the remaining solid is 1381.6 cm².
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