NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.8 – Part 3

Area of sphere

Surface Area of Sphere

Area of sphere

Q-7 Find the volume of a sphere whose surface area is Equation .

Solution:

Consider radius of the sphere to be Equation

We know that, surface area Equation

  • Equation

  • Equation Equation

  • Equation

  • Equation

  • Equation

Since we know radius r, volume is = Equation

  • Equation

  • Equation

  • Equation

Q-8 A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Equation If the cost of white-washing is Equation per square metre, find the

  1. Inside surface area of the dome.

  2. Volume of the air inside the dome.

Solution:

We know that,

  • Inside of the building is white-washed at the cost of Equation

  • Rate of white washing is Equation per square metre.

  1. Therefore, inside surface area of the dome Equation

    • Equation

    • Equation

  2. Let, radius of the dome be Equation , then surface area Equation (which we know from I. above)

  • Equation

  • Equation

  • Equation

  • Equation

Volume of the air inside the dome = Volume of the dome. However, since we know the radius, we can now calculate the volume = Equation

  • Equation

  • Equation

  • Equation

Explore Solutions for Mathematics

Sign In