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Class 8 RD Sharma Solutions – Chapter 22 Mensuration III (Surface Area And Volume Of Right Circular Cylinder) – Exercise 22.1 | Set 2
  • Last Updated : 01 Dec, 2020
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Question 11: Find the cost of plastering the inner surface of a well at Rs. 9.50 m2. If it is 21 m deep and diameter of its top is 6 m.

Solution: 

The details given about well are – 

Height of well = 21 m

Diameter of well = 6 m

So radius of well = 6/2 = 3 m



Curved surface area of cylinder = 2 * (22 /7) * r * h

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

                                                   = 396 m2

Cost of plastering the inner surface of a well = 396 * 9.50

                                                                        = Rs 3762

Question 12: A cylindrical vessel open at the top has diameter 20 cm and height 14 cm. Find the cost of tin – plating it on the inside at the rate of 50 paise per hundred square centimeters.

Solution: 

The details given about cylinder are –

Diameter of cylinder = 20 cm



So, radius = 20/2 = 10 cm

Height of cylinder = 14 cm

Total surface area of cylinder = 2 * (22/7) * r * h + (22/7) * r2 

                                               = 2 * (22/7) * 10 * 14 + (22/7) * 14 * 14

                                               = 880 + 2200/7

                                               = ((880 * 7) + 2200)/7

                                               = (6160 + 2200)/7

                                               = 8360/7 cm2

It is given that code per 100 cm2 = 50 paise

So, cost per 1 cm2 = Rs 0.005

Cost of tin-plating the area inside the vessel = (8360/7) * 0.005

                                                                        = Rs 5.97

Question 13: The inner diameter of circular well is 3.5 m. It is 10 m deep. Find the cost of plastering its inner curved surface at Rs 4 square meter.

Solution:

The details given about well are –

Inner diameter of circular well = 3.5 m

So radius = 3.5/2 m

Height of well = 10 m

Curved surface area of well = 2 * (22/7) * r * h

                                            = 2 * (22/7) * (3.5/2) * 10

                                            = 110 m2

Cost of painting 1 m2 = Rs. 4

Cost of painting 110 m2 = 4 * 110 

                                       = Rs 440

Question 14: The diameter of roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions moving once over to level a playground. What is the area of the playground?

Solution: 

The details given about roller are –

Diameter of roller = 84 cm

So radius = 84/2 = 42 cm

Length of roller = 120 cm

Curved surface area of roller = 2 * (22/7) * r * h

                                              = 2 * (22/7) * 42 * 120

                                              = 31680 cm2

Area of playground = Number of revolution * Curved surface area of roller

                                = 500 * 31680

                                = 15840000 cm2

                                          = 1584 m2 (1 m = 100 cm)

Question 15: Twenty-one cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50m high and height is 4 m, what will be the cost of cleaning them at the rate of Rs 2. 50 per square meter?

Solution: 

The details given about pillar are –

Diameter of pillar = 0.50 m

So radius = 0.50/2 = 0.25 m

Height of roller = 4 m

Curved surface area of pillar = 2 * (22/7) * r * h

                                              = 2 * (22/7) * 0.25 * 4

                                              = 44/7 m2

Curved surface area of pillar = (21 * 44)/7

                                              = 132 m2

Cost of cleaning the pillars = 2.50 * 132 

                                            = Rs 330

Question 16: The total surface area of a hollow cylinder which is open from both sides if 4620 sq cm, area of base ring is 115.5 sq cm and height 7 cm. Find the thickness of the cylinder. 

Solution: 

The details given about cylinder are –

Total surface area of hollow cylinder = 4620 cm2

Area of base ring = 115.5 cm2

Height of cylinder = 7 cm    

Let inner radius = r and outer radius = R

Area of hollow cylinder = 2 * (22/7) * (R2 – r2) + 2 * (22/7) * R * h + 2 * (22/7) * r * h

                                      = 2 * (22/7) * (R + r) (R – r) + 2 * (22/7) * r * h (R + r)

                                      = 2 * (22/7) * (R + r) * (h + R – r)

Area of base = (22/7) * R * R – (22/7) * r * r 

                     = (22/7) (R + r) * (R – r)

Total Surface area/Area of base = 4620/115.5

(2 * (22/7) (R + r) * (h + R – r))/((22/7) (R + r) (R – r)) = 4620/115.5

2 * (h + R – r)/(R – r) = 4620/115.5

R – r = thickness of cylinder

Let thickness of cylinder = t

2 * (h + t)/t = 4620/115.5

2 * h + 2 * t = 40 * t

2h = 40t – 2t

2 * 7 = 38t

14/38 = t

t = 7/19 cm

Question 17: The sum of the radius of the base and height of a solid cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, find the circumference of its base.

Solution:  

The details about the cylinder are –

Sum of radius of base and height of cylinder = 37 cm

Total surface area pf cylinder = 1628 cm2

Total surface area of cylinder = 2 * (22/7) * r * (h + r)

                                      1628 = 2 * (22/7) * r * 37   

                                     (1628 * 7)/(2 * 22 * 37) = r

                                       11396/1628 = r

                                        r = 7 m

Circumference of base = 2 * (22/7) * r

                                     = 44 m

Question 18: Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm.

Solution: 

The details given about the cylinder are –

Height of cylinder = 7.5 cm

Radius of cylinder = 3.5 cm

Total surface area of cylinder/Curved surface area of cylinder = (2 * (22/7) * r * (h + r))/(2 * (22/7) * r * h)

                                                                                                  = (h + r)/h

                                                                                                  = (7.5 + 3.5)/7.5

                                                                                                  = 11/7.5

                                                                                                  = 22/15

Question 19: A cylindrical vessel, without lid, has to be tin – coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin coating at the rate of Rs 3.50 per 1000 cm2.

Solution: 

The details given about cylinder are –

Radius of base = 70 cm

Height of cylinder = 1.4 m = 140 cm (1 m = 100 cm)

Total surface area of vessel = Area of outer side of base + Area of inner and outer curved surface

                                            = 2 ((22/7) * r * r + 2 * (22/7) * r * h)

                                            = 2 * (22/7) * r * (r + 2 * h)

                                            = 2 * (22/7) * 70 * (70 + 280)

                                            = 2 * (22/7) * 70 * 350

                                            = 154000 cm2

Cost of tin coating at the rate of Rs 3.50 per 1000 cm2 = (3.50 * 154000)/1000

                                                                                       = Rs 539

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

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