20
From a solid cylinder of height $20$ cm and diameter $12$ cm, a conical cavity of height $8$ cm and radius $6$ cm is hallowed out. Find the total surface area of the remaining solid.
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Height of cylinder $h = 20$ cm
radius of cylinder $= 6$ cm $=$ Radius of cone
Height of cone $= 8$ cm
Slant height $l = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = 10$ cm
Surface area of remaining solid
$= CSA \text{ of cylinder} + CSA \text{ of cone} + \text{Area of base of cylinder}$
$= 2\pi rh + \pi rl + \pi r^2 = \pi r[2h + l + r]$
$= \frac{22}{7} \times 6[2 \times 20 + 10 + 6] = \frac{22}{7} \times 6 \times 56$
$= 1056 \text{ cm}^2$
radius of cylinder $= 6$ cm $=$ Radius of cone
Height of cone $= 8$ cm
Slant height $l = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = 10$ cm
Surface area of remaining solid
$= CSA \text{ of cylinder} + CSA \text{ of cone} + \text{Area of base of cylinder}$
$= 2\pi rh + \pi rl + \pi r^2 = \pi r[2h + l + r]$
$= \frac{22}{7} \times 6[2 \times 20 + 10 + 6] = \frac{22}{7} \times 6 \times 56$
$= 1056 \text{ cm}^2$