Curved Surface Area Solution2





In this page curved surface area solution2 we are going to see solution of some practice questions.

Question 4

A mansion has 12 right cylindrical pillars each having radius 50 cm and height 3.5 m. Find the cost to paint the lateral surface of pillars at $ 20 per square meter.

Solution:

The pillars of the mansion are in the shape of cylinder

Curved surface area of one pillar = 2 Π r h

          radius = 50 cm

                   = 0.5 m

         height = 3.5 m

Curved surface area of one pillar = 2 x (22/7) x 0.5 x 3.5

                                               = 2 x 22 x 0.5 x 0.5

                                               = 11 m²

Curved surface of 12 pillars = 12 x 11

                                        = 132 m²

Cost to paint per m² = $ 20

 Total cost = 20 x 132

                = $ 2640   

Required cost of painting 132 m² is $ 2640


Question 5

The total surface area of a solid right circular cylinder are 231 cm². Its curved surface area is two thirds of the total surface area. Find the radius and height of the cylinder.

Solution:

Curved surface area = (2/3) x Total surface area

                      2 Π r h  = (2/3) x 231

                      2 Π r h  = 2 x 77

                      2 Π r h  = 154

Total surface area of the cylinder = 231 cm²                        

                                      2 Π r (h + r) = 231

                                      2 Π r h + 2 Π r²  = 231

                                       154 + 2 Π r²  = 231

                                                 2 Π r²  = 231 - 154

                                                 2 Π r²  = 77

                                  2 x (22/7) x r²  = 77

                                                r²  = 77 x (7/22) x (1/2)

                                                r²  = (7/2) x (7/2)

                                         r = (7/2) cm

                 2 Π r h  = 154

      x (22/7) x (7/2) x= 154

                                   h = 154 x (1/2)  x (7/22) x (2/7)

                                   h = 7 cm

Radius = 3.5 cm

Height = 7 cm

curved surface area solution2 curved surface area solution2