Vessel P is a cylinder of radius 6 cm and height 10 cm. Vessel Q is a cylinder of radius 6 cm and height 6 cm whose bottom is a hemisphere of radius 6 cm bulging outward below it. Which vessel holds more, and by how much? (Take π = 22/7.)

Question

Accepted Answer

They hold exactly the same amount. P = \π (36)(10) = 22/7 × 360 = 1131.43 cm³. For Q, cylinder = 22/7(36)(6) = 678.86 cm³ and the hemisphere below adds 2/3\π r^3 = 2/3 × 22/7 × 216 = 452.57 cm³, giving 1131.43 cm³. They are equal, because a hemisphere of radius r holds as much as a cylinder of radius r and height 2r/3 = 4 cm, and 6 + 4 = 10. The other options quote the hemisphere's volume, or half of it, as a difference that does not exist.

Vessel P is a cylinder of radius 6 cm and height 10 cm. Vessel Q is a cylinder of radius 6 cm and height 6 cm whose bottom is a hemisphere of radius 6 cm bulging outward below it. Which vessel holds more, and by how much? (Take π = 22/7.)

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Volume of Combined Solids practice