## RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1

Other Exercises

- RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1
- RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2
- RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder VSAQS
- RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQS

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 5.

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

Solution:

Total surface area of a hollow cylinder open from both sides = 4620 cm^{2}

Area of base of ring = 115.5 cm^{2}

Height (h) = 7 cm

Let outer radius (R) = R

and inner radius = r

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 = \(\frac { 1.5 }{ 2 }\) = 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 = \(\frac { 1 }{ 3 }\) 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 \(\frac { 1 }{ 12 }\) of steel actually used was wasted in making the closed tank? [NCERT]

Solution:

Diameter of a cylinderical tank = 4.2 m

Hope given RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 are helpful to complete your math homework.

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