NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.4 – Part 2
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 .
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 =