A solid cuboid has dimensions 14cm × 18cm × 24cm. A hemisphere of radius 3.5 cm is cut from the centre of each face of cuboid. What is the total surface area (in cm2) of the remaining solid?
Show answer & explanation
Correct answer: D
Explanation
The correct option is 4.
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 × 2πR2 − 6 × π R2 = 2(lb + bh + lh) + 6 × πR2.
⇒ 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 = 2271cm2