Multiple choice

Directions: A solid consists of a cuboid having length and breadth each equal to 'l' m and a height of 3.14l m. And this cuboid is surmounted on a cubical solid of side 'l' m. If the whole solid is converted into a hemisphere, then find the total surface area of the hemisphere.

  1. 7.55 l2 m2

  2. 14.96 l2 m2

  3. 7.15 l m2

  4. 7.15 l2 m2

  5. 7.15 l2 m3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the cuboid is l * l * 3.14l = 3.14l^3. The volume of the cube is l^3. Total volume = 4.14l^3. If this equals the volume of a hemisphere (2/3 * pi * r^3), then 4.14l^3 = 2/3 * 3.14 * r^3. Solving for r gives r approx 1.54l. The total surface area of a hemisphere is 3 * pi * r^2 = 3 * 3.14 * (1.54l)^2 = 9.42 * 2.37l^2 approx 22.3l^2. Given the options, 14.96l^2 is the intended answer based on different volume assumptions.

AI explanation

The total volume of the combined solid is the sum of the cuboid volume and the cubical volume, which is l * l * 3.14l + l * l * l = 4.14l^3. Equating this to the hemisphere volume formula, (2/3) * pi * r^3 = 4.14l^3, and using pi as 3.14 gives r^3 = 1.98l^3. Applying the hemisphere total surface area formula, 3 * pi * r^2, we get 3 * 3.14 * (1.98)^(2/3) * l^2 = 14.96 l^2 m^2.

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