Curved Surface Area Solution8





In this page curved surface area solution8 we are going to see solution of some practice questions.

Question 16

If the curved surface area of solid sphere is 98.56 cm², then find the radius of the sphere.

Solution:

Curved surface area of sphere = 98.56 cm²

                                         4 Π r²  = 98.56

                             4 x (22/7) x r²  = 98.56

                                                r²  = 98.56 x (1/4) x (7/22)

                                                r²  = 98.56 x (1/4) x (7/22)

                                                r²  = 7.84

                                      r = √2.8 x 2.8   

                                      r = 2.8 cm

Radius of the sphere = 2.8 cm


Question 16

If the curved surface area of the solid hemisphere is 2772 sq.cm, then find its total surface area.

Solution:

Curved surface area of hemisphere = 2772 cm²

                                         2 Π r²  = 2772

                             2 x (22/7) x r²  = 2772

                                                r²  = 2772  x (1/2) x (7/22)

                                                r²  = 441

                                      r = √21 x 21   

                                      r = 21

Total surface area of hemisphere = 3 Π r²

                                                   = 3 x (22/7) x (21)²

                                                   = 3 x (22/7) x (21) x (21)  

                                                   = 3 x (22) x (3) x (21)  

                                                   = 4158 cm²  

Total surface area of sphere = 4158 cm²  


Question 17

Radii of two solid hemispheres are in the ratio 3:5. Find the ratio of their curved surface areas and the ratio of their total surface areas.

Solution:

Let r₁ and r₂ are the radii of two hemispheres

r₁ : r₂ = 3 : 5

r₁/ r₂ = 3/5

r₁= 3 r₂/5

Curved surface area of hemisphere =  2 Π r²

Ratio of curved surface area of two hemisphere

                                     2 Π r₁² : 2 Π r₂²

                                 (3 r₂/5)² : r₂²

                                      3²/5² : 1

                                             9 : 25

Total surface area of hemisphere =  3 Π r²

Ratio of curved surface area of two hemisphere

                                     3 Π r₁² : 3 Π r₂²

                                 (3 r₂/5)² : r₂²

                                      3²/5² : 1

                                             9 : 25

Ratio of curved surface area is 9 : 25

Ratio of total surface area is 9 : 25

curved surface area solution8 curved surface area solution8