Combination of Solids Solution1





In this page combination of solids solution1 we are going to see solution some practice questions of the worksheet combination of solid worksheet1.

Question 1:

A play top is in the form of a hemisphere surmounted on a cone. The diameter of the hemisphere is 3.6 cm. The total height of the play top is 4.2 cm. Find its total surface area.

Solution:

Let r and h are radius and height of the cone.

diameter of the hemisphere = 3.6 cm

radius of hemisphere (r) = (3.6)/2 = 1.8 cm

total height of the play top = 4.2cm

radius of hemisphere + height of cone = 4.2

                            1.8 + h = 4.2

                                    h = 4.2 - 1.8

                                    h = 2.4 cm

Now we are going to find slant height of cone

                         L² = r² + h²

                             = (1.8)² + (2.4)²

                             = 3.24 + 5.76

                        L² = 9

                        L = √3 x 3

                        L = 3 cm

To find the total surface area of the play top we have to find the sum of curved surface area of hemisphere and curved surface area of cone.

Total surface area of play top = C.S.A of hemisphere + C.S.A of cone

                                          =  2 Π r² +  Π r L

                                          =  Π r [2 r + L]

                                          = Π x (1.8) [2(1.8) + 3] 

                                          = Π x (1.8) [3.6 + 3]

                                          = Π x (1.8) [6.6]

                                          = 11.88 Π cm²

Total surface area of the play top = 11.88 Π cm²  

combination of solids solution1 combination of solids solution1