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.Options280104266.12162

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 base of the cone) is 6.5 cm, we can calculate the volume of the hemisphere as follows:

V_hemisphere = 2/3 * π * (6.5 cm)³ = 2/3 * π * 274.625 cm³ = 183.259 cm³.

The total height of the doll is 12.5 cm, but this includes the radius of the hemisphere, so 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 = 1/3 * π * 42.25 cm² * 6 cm = 84.78 cm³.

Adding these two volumes together gives the total volume of the doll:

V_total = V_hemisphere + V_cone = 183.259 cm³ + 84.78 cm³ = 268.039 cm³.

So, the volume of the wooden doll is approximately 268 cm³.