Radius =1cm
height =1cm
volume of cone and hemisphere = 1/3πr^2h + 2/3πr^3
1/3πr^2 (h+2r)
1/3×22/7×1×1(1+2×1)
1/3×22/7×3
22/7anwer

Shape of the Solid

The solid is composed of a cone standing on top of a hemisphere. Both the cone and the hemisphere have radii equal to 1 cm. The height of the cone is equal to its radius.

Calculating the Volume

To calculate the volume of the solid, we need to find the volume of the cone and the volume of the hemisphere separately, and then add them together.

Volume of the Cone

The formula for the volume of a cone is given by V = (1/3) * π * r^2 * h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the cone, and h is the height of the cone.

In this case, the radius of the cone is 1 cm, and the height of the cone is also 1 cm. Plugging these values into the formula, we get:

V_cone = (1/3) * π * (1 cm)^2 * (1 cm)
= (1/3) * π * 1 cm^2 * 1 cm
= (1/3) * π * 1 cm^3
= (1/3) * π cm^3
≈ 1.047 cm^3

Volume of the Hemisphere

The formula for the volume of a hemisphere is given by V = (2/3) * π * r^3, where V is the volume, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the hemisphere.

In this case, the radius of the hemisphere is 1 cm. Plugging this value into the formula, we get:

V_hemisphere = (2/3) * π * (1 cm)^3
= (2/3) * π * 1 cm^3
= (2/3) * π cm^3
≈ 2.094 cm^3

Total Volume of the Solid

To find the total volume of the solid, we add the volume of the cone and the volume of the hemisphere:

V_total = V_cone + V_hemisphere
= 1.047 cm^3 + 2.094 cm^3
≈ 3.141 cm^3

Therefore, the volume of the solid is approximately 3.141 cm^3.