In this chapter, we provide RD Sharma Solutions for Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Maths pdf, free RD Sharma Solutions for Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Maths book pdf download. Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 9 |

Subject | Maths |

Chapter | Chapter 19 |

Chapter Name | Surface Areas and Volume of a Circular Cylinder |

Exercise | Ex 19.1 |

**RD Sharma Solutions for Class 9 Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Download PDF**

Question 1.

Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m, find its height. [NCERT]

Solution:

Curved surface area of a cylinder = 4.4 m^{2}

Radius (r) = 0.7 m

Question 2.

In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system. [NCERT]

Solution:

Diameter of the pipe = 5 cm

Question 3.

A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m^{2}. [NCERT]

Solution:

Diameter of cylindrical pillar = 50 cm

Question 4.

It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same? [NCERT]

Solution:

Height of cylinder (h) = 1 m = 100 cm

Diameter of box = 140 cm

Question 6.

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:

Radius of the cylinder (r) = 3.5 cm

and height (h) = 7.5 cm

Total surface area = 2πr (h + r)

and curved surface area = 2πrh

Question 7.

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 ₹3.50 per 1000 cm^{2}.

Solution:

Radius of the base of a cylindrical vessel (r) = 70 cm

and height (h) = 1.4 m = 140 cm

Total surface area (excluding upper lid) on both sides = 2πrh x 2 + πr^{2} x 2

Question 8.

The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find:

(i) inner curved surface area.

(ii) the cost of plastering this curved surface at the rate of ₹40 per m^{2}. [NCERT]

Solution:

Inner diameter of a well = 3.5 m

Question 9.

The students of a Vidyalaya were asked to participate s a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each pen holder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? [NCERT]

Solution:

Radius of cylinderical pen holder (r) = 3 cm

Height (h) = 10.5 cm

∴ Surface area of the pen holder

Question 10.

The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a play¬ground, find the cost of levelling this ground at the rate of 50 paise per square metre.

Solution:

Diameter of a roller = 1.5 m

∴ Radius = 1.52 = 0.75 m = 75 cm

and length (h) = 84 cm

Question 11.

Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m. What will be the cost of cleaning them at the rate of ₹2.50 per square metre? [NCERT]

Solution:

Number of pillars = 20

Diameter of one pillar = 0.50 m

Question 12.

A solid cylinder has total surface area of 462 cm^{2}. Its curved surface area is one- third of its total surface area. Find the radius and height of the cylinder.

Solution:

Total surface of solid cylinder = 462 cm^{2}

Curved surface area = 13 of total surface area

Question 13.

The total surface area of a hollow metal cylinder, open at both ends of external radius 8 cm and height 10 cm is 338 π cm^{2}. Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.

Solution:

Total surface area of a hollow metal cylinder = 338π cm^{2}

Let R be the outer radius, r be inner radius and h be the height of the cylinder of the cylinder

∴ 2πRh + 2πrh + 2πR^{2} – 2πr^{2} = 338π

R = 8 cm, h = 10 cm

⇒ 2πh (R + r) + 2π(R^{2} – r^{2}) = 338π

⇒ Dividing by 2π , we get

⇒ h(R + r) + (R^{2} – r^{2}) = 169

⇒ 10(8 + r) + (8 + r) (8 – r) = 169

⇒ 80 + 10r + 64 – r^{2} = 169

⇒ 10r – r^{2} + 144 – 169 = 0

⇒ r^{2} – 10r + 25 = 0

⇒ (r-5)^{2} = 0

⇒ r = 5

∴ Thickness of the metal = R – r = 8 – 5 = 3 cm

Question 14.

Find the lateral curved surface area of a cylinderical petrol storage tank that is 4.2m in diameter and 4.5 m high. How much steel was actually used, if 112 of steel actually used was wasted in making the closed tank? [NCERT]

Solution:

Diameter of a cylinderical tank = 4.2 m

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**All Subject NCERT Solutions For Class 9**

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