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

Curved surface area of hemisphere is half of sphere.

Curved Surface Area and Total Surface Area of Sphere

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 = Equation

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

Hemisphere of radius Equation

Therefore, total surface area of hemisphere = Equation = Equation = Equation

Q-4 The radius of a spherical balloon increases from Equation to Equation 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 Equation and the increased radius of balloons is Equation . Where, Equation

Therefore, ratio of the surface area

  • Equation

  • Equation

  • Equation

So, the surface areas are in ratio Equation .

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

Solution:

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

Radius of the bowl (r) Equation ( Equation )

Therefore, curved surface area of the hemispherical bowl

  • Equation

  • Equation

  • Equation

Tin-plating costs for 100 cm2 is Equation

So, cost of tin plating Equation

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

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

Consider, Equation be the radius of the sphere.

We know that surface area = Equation

  • Therefore, Equation

  • Equation

  • Equation

  • Equation

  • Equation

  • Equation

  • Equation

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