Multiple choice

Directions: A solid consists of a frustum having height '3a', bottom radius '2a' and top radius 'a' and a cylinder on the top of frustum with same radius and height '2a'. If oil is put in the solid from a cube of edge '4a' full of oil, how much oil will be left in the cube? (Use π = 3.14)

  1. 34.54a3

  2. 35.74a3

  3. 23.54a3

  4. 33.46a3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of frustum = (1/3) * pi * h * (R^2 + r^2 + R*r) = (1/3) * 3.14 * 3a * (4a^2 + a^2 + 2a^2) = 3.14 * 7a^3 = 21.98a^3. Volume of cylinder = pi * r^2 * h = 3.14 * a^2 * 2a = 6.28a^3. Total volume = 21.98 + 6.28 = 28.26a^3. Cube volume = (4a)^3 = 64a^3. Remaining oil = 64 - 28.26 = 35.74a^3.

AI explanation

The capacity of the solid is the sum of the frustum volume and the cylinder volume. The frustum volume is one third times pi times 3a times ((2a) squared plus 2a times a plus a squared), which equals 7 times pi times a cubed, or 21.98a cubed. The cylinder volume is pi times a squared times 2a, equaling 2 times pi times a cubed, or 6.28a cubed, so the total capacity is 28.26a cubed. Since the cube holds 64a cubed, subtracting the capacity leaves 35.74a cubed of oil.

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