A solid wooden doll is in the shape of a right circular cone mounted on a hemisphere with same radius. If the radius of the hemisphere is 6.5 cm and the total height of the toy is 12.5 cm, find the volume of the wooden doll.Options162104280266.12

The volume of the wooden doll can be calculated by adding the volume of the hemisphere and the volume of the cone.

The volume V of a hemisphere is given by the formula V = 2/3 * π * r³, where r is the radius of the hemisphere.

The volume V of a cone is given by the formula V = 1/3 * π * r² * h, where r is the radius of the base of the cone and h is the height of the cone.

Given that the radius of the hemisphere (and also the cone, since they have the same radius) is 6.5 cm, we can calculate the volume of the hemisphere as follows:

V_hemisphere = 2/3 * π * (6.5 cm)³ = 289.53 cm³

The total height of the toy is 12.5 cm, but this includes the height of the hemisphere, which is equal to the radius. Therefore, the height of the cone is 12.5 cm - 6.5 cm = 6 cm. We can calculate the volume of the cone as follows:

V_cone = 1/3 * π * (6.5 cm)² * 6 cm = 132.73 cm³

Finally, the total volume of the wooden doll is the sum of the volume of the hemisphere and the volume of the cone:

V_total = V_hemisphere + V_cone = 289.53 cm³ + 132.73 cm³ = 422.26 cm³

So, the volume of the wooden doll is approximately 422.26 cubic centimeters. None of the options provided match this result.