Question

A vessel, in the form of an inverted cone, is
filled with water to the brim. Its height is
32 cm and diameter of the base is 25.2 cm.
Six equal solid cones are dropped in it, so
that they are fully submerged. As a result,
one-fourth of water in the original cone
overflows. What is the volume of each of the
solid cones submerged ?​

Answer 1

Height of Cone = 32 cm

Diameter of Cone = 25.2 cm

Radius of Cone = 12.6 cm

Now If we will find the Volume of Cone in Liters then we will be able to find the Volume of each cone.

Volume of Cone = πr²h/3

V = π (12.6)(12.6)(32)/3 cm³

V = 1693.44π cm³

Converting cm³ to Liters.

V = 1.69344π L

Now, As given one-fourth over flow.

Volume of small cones =1/4Volume of water×1/6

V = 1/24 × 1.69344

V = 0.07056 L

Again, Converting L to cm³

V = 70.56 cm³

Hence,

Volume of each cone = V = 70.56 cm³