Multiple choice

Volume of the cylinder is 3564 m³ Radius of the cylinder is equal to the side of a square whose area is 81 sq m. Height of the cuboid is equal to the height of the cylinder. The Width of the cuboid is half of the height of the cylinder. Total surface area of the cuboid is 700 sq m. Find the volume of the cuboid.

  1. 1312 cu. m

  2. 1224 cu. m

  3. 1172 cu. m

  4. 1176 cu m
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D Correct answer
Explanation

Cylinder radius = sqrt(81) = 9. Cylinder volume = pi * r^2 * h = 3564. h = 3564 / (pi * 81) = 14. Cuboid height = 14, width = 7. Surface area = 2(lw + lh + wh) = 700. 2(l*7 + l*14 + 7*14) = 700. 21l + 98 = 350. 21l = 252, l = 12. Volume = l * w * h = 12 * 7 * 14 = 1176.

AI explanation

The square's area is 81 sq m, so the cylinder's radius is 9 m. Using the cylinder volume formula V = pi * r^2 * h, we have 3564 = 22/7 * 81 * h, which gives h = 14 m. The cuboid's width is half the cylinder's height, making it 7 m, and its height matches the cylinder's height at 14 m. Using the total surface area formula for a cuboid, TSA = 2(lb + bh + hl), we set 700 = 2(l * 7 + 7 * 14 + 14 * l). Solving 350 = 21l + 98 gives 21l = 252, so the length is 12 m. The volume of the cuboid is then 12 * 7 * 14 = 1176 cu m.

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