NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.4 – Part 2
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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 =
Q3 Find the total surface area of a hemisphere of radius. (Use)Solution:
Hemisphere of radius
Therefore, total surface area of hemisphere = = =
Q4 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 .
Q5 A hemispherical bowl made of brass has inner diameter . Find the cost of tinplating 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
Tinplating costs for 100 cm^{2} is
So, cost of tin plating
Finally, total cost of tinplating the hemisphere bowl with area cm^{2 }is
Q6 Find the radius of a sphere whose surface area is.Solution:
Consider, be the radius of the sphere.
We know that surface area =

Therefore,





