Question 46

A solid cuboid has dimensions $$14 cm \times 18 cm \times 24 cm$$. A hemisphere of radius 3.5 cm is cut from the centre of each face of cuboid. What is the total surface area (in $$cm^2$$)of the remaining solid?

Solution

Total surface area of the remaining solid = Total surface area of cuboid + 6 × CSA of hemisphere - 6 × Area of the circular base

⇒ $$2(lb+bh+lh)+6\times2\pi R^2-6\times\pi\ R^2=2(lb+bh+lh)+6\times\pi R^2.$$

⇒ 2 × (14 × 18 + 18 × 24 + 24 × 14) + 6 × 22/7 × 3.5 × 3.5

⇒ 2 × 12 × (7 × 3 + 18 × 2 + 2 × 14) + 6 × 22 × 0.5 × 3.5

⇒ $$24 × 85 + 231 = 2271 cm^2$$

D is correct choice.

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