NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.4 – Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Curved Surface Area of Hemisphere is Half of Sphere

Curved surface area of hemisphere is half the area of sphere. The total surface area also includes the base of radius r at the bottom therefore TSA of Sphere =

Q-3 Find the total surface area of a hemisphere of radius . (Use ) Solution:

Hemisphere of radius

Therefore, total surface area of hemisphere = = =

Q-4 The radius of a spherical balloon increases from to as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases. Solution:

Now, the initial radius is and the increased radius of balloons is . Where,

Therefore, ratio of the surface area

So, the surface areas are in ratio .

Q-5 A hemispherical bowl made of brass has inner diameter . Find the cost of tin-plating it on the inside at the rate of .

Solution:

A bowl is a hemisphere with no base. So we are interested only in the curved surface area.

Radius of the bowl (r) ()

Therefore, curved surface area of the hemispherical bowl

Tin-plating costs for 100 cm2 is

So, cost of tin plating

Finally, total cost of tin-plating the hemisphere bowl with area cm2 is

Q-6 Find the radius of a sphere whose surface area is . Solution:

Consider, be the radius of the sphere.

We know that surface area =

  • Therefore,

Developed by: