Multiple choice

A city designs a water storage system. This system features a unique water tank in the form of a right circular cylinder. The cylinder is carefully crafted to fit inside a spherical container with a radius of 6 metres. The height of the cylinder is 10 metres. What is the amount of water that this specific cylindrical tank is capable of holding? (1 cubic metre = 1000 litres)

  1. 60,000 litres

  2. 1,10,000 litres

  3. 3,45,400 litres

  4. 5,55,000 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The cylinder fits inside a sphere of radius 6. The cylinder's height is 10, so its radius r satisfies r^2 + (h/2)^2 = R_sphere^2. r^2 + 5^2 = 6^2, so r^2 = 36 - 25 = 11. Volume = pi * r^2 * h = 3.14159 * 11 * 10 = 345.57 cubic meters. 345.57 * 1000 = 345,570 litres. Option C is the closest.

AI explanation

A cylinder of height 10 m inscribed in a sphere of radius 6 m has half its height at 5 m from the center, so using the Pythagorean theorem, its radius squared is 6 squared minus 5 squared, which equals 11. The volume of the cylindrical tank is pi times r squared times h, giving pi times 11 times 10, which equals 110 pi cubic metres. Since 1 cubic metre is 1000 litres and using pi as 3.14, the capacity is 110 times 3.14 times 1000, which gives 345,400 litres.

Keep practicing — related questions