Multiple choice

A solid right circular cone of radius 4 cm and height 7 cm is put inside a cylindrical vessel of radius 5 cm and height 8 cm. How much water, in cubic centimetres, will be required to fill the cylindrical vessel completely?

  1. 1022.48

  2. 1533.72

  3. 511.24

  4. 255.62
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 25 * 8 = 200 * pi. Volume of cone = 1/3 * pi * r^2 * h = 1/3 * pi * 16 * 7 = 112/3 * pi. Water needed = 200*pi - 37.33*pi = 162.67 * pi = 511.24.

AI explanation

The volume of the cylindrical vessel is found using the formula pi*r^2*h, which equals (22/7) * 5^2 * 8 = 628.57 cubic centimetres. The volume of the solid cone placed inside is calculated as (1/3)*pi*r^2*h, giving (1/3) * (22/7) * 4^2 * 7 = 117.33 cubic centimetres. Subtracting the cone's volume from the cylinder's volume gives the required water volume, which is 628.57 minus 117.33 equals 511.24 cubic centimetres.

Keep practicing — related questions