Question

A solid toy is in the form of a hemisphere surmounted by a cone of same radius. The height of cone is 3 cm and the diameter of base is 8 cm. Determine the volume and surface area of the toy.[ Use pie = 22 /7 ]​

Answer 1

Answer:

Volume of toy is 184.4 cm³ and Surface area of toy is 163.43 cm²

Step-by-step explanation:

Given : Hemisphere diameter = d = 8 cm , Radius R =8/2 = 4 cm

           Height of cone = 8 cm

           Volume of toy = ?

           Surface area of toy = ?

Solution : Volume of toy = volume of hemisphere + volume of cone

                                        = 2/3 x π x R³ + 1/3 x π x R² x H

                                        = 1/3πR² ( 2R + H)

                                        = 1/3 x 22/7 x 4² x ( 2x4 + 3)

                                        = 1/3 x 22/7 x 16 x 11

                                        = 184.4 cm³

Surface area of toy = CSA of hemisphere + LSA of cone

                                = 2πR² + πR x $\sqrt{h^{2}+R^{2} }$

                                = πR ( 2R + $\sqrt{h^{2}+R^{2} }$)

                                = 22/7 x 4 x ( 2x4 + $\sqrt{3^{2} + 4^{2} }$)

                                = 22/7 x 4 x (8 + 5)

                                = 22/7 x 4 x 13

                                = 163.43 cm²