Multiple choice

A metallic right circular cone of height 9 cm and base radius 7 cm is melted to form a cuboid with two sides measuring 11 cm and 6 cm. The third side of the cuboid measures

  1. 5 cm

  2. 6 cm

  3. 7 cm

  4. 9 cm

  5. 10 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cone = 1/3 * pi * r^2 * h = 1/3 * 22/7 * 7^2 * 9 = 462. Volume of cuboid = 11 * 6 * x = 66x. 66x = 462, x = 7.

AI explanation

The volume of the cone is found using the formula V = (1/3)πr²h, which gives (1/3) × (22/7) × 7² × 9 = 462 cubic cm. Because the cone is melted to form a cuboid, their volumes are equal, so 11 × 6 × third side = 462. Solving 66 × third side = 462 gives the third side as 7 cm.

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