## RD Sharma Class 9 Solutions Chapter 21 Surface Areas and Volume of a Sphere Ex 21.1

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 21 Surface Areas and Volume of a Sphere Ex 21.1

Other Exercises

- RD Sharma Class 9 Solutions Chapter 21 Surface Areas and Volume of a Sphere Ex 21.1
- RD Sharma Class 9 Solutions Chapter 21 Surface Areas and Volume of a Sphere Ex 21.2
- RD Sharma Class 9 Solutions Chapter 21 Surface Areas and Volume of a Sphere VSAQS
- RD Sharma Class 9 Solutions Chapter 21 Surface Areas and Volume of a Sphere MCQS

Question 1.

Find the surface area of a sphere of radius.

(i) 10.5 cm

(ii) 5.6 cm

(iii) 14 cm

Solution:

In a sphere,

(i) Radius (r) = 10.5 cm

Surface area = 4πr^{2}

Question 2.

Find the surface area of a sphere of diameter

(i) 14 cm

(ii) 21 cm

(iii) 3.5 cm

Solution:

(i) Diameter of a sphere = 14 cm

Radius (r) = \(\frac { 14 }{ 2 }\) = 7 cm

Question 3.

Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm. [Use π = 3.14]

Solution:

(i) Radius of hemisphere = 10 cm

∴ Total surface area of hemisphere = 2πr^{2}

= 2 x 3.14 x 10 x 10 cm^{2}

= 628 cm^{2}

(ii) Total surface area of solid hemisphere

= 3πr^{2} = 3 x 3.14 x 10 x 10 cm^{2}

= 942 cm^{2}

Question 4.

The surface area of a sphere in 5544 cm^{2}, find the diameter.

Solution:

Let r be the radius of a sphere, then Surface area = 4πr^{2}

Question 5.

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹4 per 100 cm^{2}. [NCERT]

Solution:

Inner diameter of a hemispherical bowl = 10.5 cm

Question 6.

The dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of painting it at the rate of ₹2 per sq. m.

Solution:

Radius of dome (hemispherical) = 63 dm

Area of curved surface

Question 7.

Assuming the earth to be a sphere of radius 6370 km, how many square kilometres is area of the land, if three-fourth of the earth’s surface is covered by water?

Solution:

Radius of earth (sphere) = 6370 km

Water on the earth = \(\frac { 3 }{ 4 }\) % total area

Question 8.

A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved surface area of the shape if the length of the shape be 7 cm.

Solution:

Total height of the so formed shape = 7 cm

Question 9.

The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Solution:

Diameter of moon = \(\frac { 1 }{ 4 }\) of diameter of earth

Let radius of earth = r km

Then radius of moon = \(\frac { 1 }{ 4 }\) r km

Now surface area of earth = 4πr^{2}

Question 10.

A hemi-spherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is ₹5 per 100 cm^{2}. [NCERT]

Solution:

Circumference of the base of dome (r) = 17.6 m

Question 11.

A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at ₹7 per 100 cm^{2}.

Solution:

Diameter of toy = 16 cm

Radius (r) = \(\frac { 16 }{ 2 }\) = 8 cm

Height of conical part (h) = 15 cm

Question 12.

A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 1.4 m and its length be 8 m, find the cost of painting it on the outside at the rate of ₹10 per m^{2}.

Solution:

Diameter of the tank = 1.4 m

∴ Radius (r) = \(\frac { 1.4 }{ 2 }\) m = 0.7 m

and height of cylindrical portion = 8m

Question 13.

The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm^{2} and black paint costs 5 paise per cm^{2}. [NCERT]

Solution:

Diameter of each spheres = 21 cm

∴ Radius (R) = \(\frac { 21 }{ 2 }\) cm

Radius of each cylinder (r) = 1.5 cm

and height (h) = 7 cm

Now surface area of one sphere = 4πR^{2}

Hope given RD Sharma Class 9 Solutions Chapter 21 Surface Areas and Volume of a Sphere Ex 21.1 are helpful to complete your math homework.

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