Question

13 cm 7 cm NOT TO SCALE The diagram shows a solid made up of a hemisphere and a cone. The base radius of the cone and the radius of the hemisphere are each 7 cm. The height of the cone is 13 cm. (a) (i) Calculate the total volume of the solid. [The volume of a hemisphere of radius r is given by V = ¹.] [The volume of a cone of radius r and height h is given by Varh.​

Answer 1

Explanation:

V = 2/3 * pi * r3 gives the volume of a hemisphere of radius r.

V = 1/3 * pi * r2 * h gives the volume of a cone with radius r and height h.

We may compute the volume of both forms using the hemisphere's radius and the cone's base radius of 7 cm:

Hemisphere Volume = 2/3 * pi * (7 cm)3 = (14/3) * pi * 343 cm3 = 615.75 cm3

Cone Volume = 1/3 * pi * (7 cm)2 * 13 cm = 49 * pi * cm3 = 153.94 cm3

To get the overall volume of the solid, sum the volumes of the hemisphere and cone:

Volume total = 615.75 cm3 + 153.94 cm3 = 769.69 cm3

As a result, the total volume of the solid is 769.69 cm3.