Question : From a solid cylindrical wooden block of height 18 cm and radius 7.5 cm, a conical cavity of the same height and radius is taken out. What is the total surface area (in cm2) of the remaining solid?
Option 1: $270 \pi$
Option 2: $416.25 \pi$
Option 3: $326.25 \pi$
Option 4: $472.5 \pi$
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Correct Answer: $472.5 \pi$
Solution :
According to the question
⇒ Area of base = πr
2
Now,
⇒ Slant height, $l=\sqrt{h^{2}+r^{2}}=\sqrt{18^{2} + 7.5^{2}}=\sqrt{324 + 56.25}=\sqrt{380.25} = 19.5$
The curved surface of the cone = πrl
= $π × 7.5 × 19.5$
= $146.25 π$
The surface area of the cylinder = 2πrh
= $2π × 7.5 × 18$
= $270 π$
Area of the base of the cylinder = πr
2
= $π$ × (7.5)
2
= $56.25 π$
The total surface area of the remaining solid
= $146.25π + 270π + 56.26π$
= $472.5 π$
Hence, the correct answer is $472.5π$.
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