Curved Surface Area Solution9





In this page curved surface area solution9 we are going to see solution of some practice questions.

Question 19

Find the curved surface area and total surface of a hollow hemisphere whose outer and inner radii are 4.2 cm and 2.1 cm respectively.

Solution:

Inner radius (r) = 2.1 cm

Outer radius (R) = 4.2 cm

Curved surface area = 2Π (R² + r²) 

                              = 2 x Π x [(4.2)² + (2.1)²]

                              = 2 x Π x (17.64 + 4.41)

                              = 2 x Π x (22.05)

                              = 44.1 Π cm²

Total surface area = 2Π (R² + r²) + Π (R² - r²)

                              = 44.1 Π + Π x [(4.2)² - (2.1)²]

                              = 44.1 Π + Π (17.64 - 4.41)

                              = 44.1 Π + Π (13.23)

                              = 44.1 Π + 13.23 Π

                              = 57.33 Π cm²


Curved surface area = 44.1 Π cm²

Total surface area = 57.33 Π cm²


Question 20

The inner curved surface area of a hemisphere dome of a building needs to be painted . If the circumference of the base is 17.6 m,find the cost of painting it at the rate of $5 per sq.m

Solution:

Circumference of the base = 17.6 m

                               2 Π r = 17.6

                   2 x (22/7) x r = 17.6

                                   r = 17.6 (1/2) (7/22)

                                   r = 2.8 m

Curved surface area of hemisphere = 2 Π r²

                                                   = 2 (22/7) (2.8)²

                                                   = 49.28 m²

Cost of painting $ 5 per square meter

 Total cost = 5 x 49.28

               = $ 246.40

Outer radius (R) = 4.2 cm

curved surface area solution9 curved surface area solution9