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 154cm2 .


Consider radius of the sphere to be rcm

We know that, surface area =154cm2

  • 4πr2=154

  • 4×227×r2=154 (π=227)

  • r2=154×74×22

  • r2=12.25

  • r=3.5cm

Since we know radius r, volume is = 43πr3

  • =(43×227×3.5×3.5×3.5)cm3

  • =5393cm3

  • =179.66cm2

Q-8 A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs498.96 If the cost of white-washing is Rs2.00 per square metre, find the

  1. Inside surface area of the dome.

  2. Volume of the air inside the dome.


We know that,

  • Inside of the building is white-washed at the cost of Rs498.96

  • Rate of white washing is Rs2.00 per square metre.

  1. Therefore, inside surface area of the dome =TotalcostofwhitewashingRateofwhitewashing

    • (498.962.00)m2

    • 249.48m2

  2. Let, radius of the dome be r , then surface area =2πr2=249.48 (which we know from I. above)

  • 2×227×r2=249.48

  • r2=249.48×72×22=39.69

  • r2=39.69

  • r=6.3m

Volume of the air inside the dome = Volume of the dome. However, since we know the radius, we can now calculate the volume = 23πr3

  • =(23×227×6.3×6.3×6.3)m3

  • =(4421×250.047)

  • =523.9m3(approx.)

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