NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.3 – Part 1

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Q-1 Diameter of the base of a cone is 10.5cm and its slant height is 10cm . Find its curved surface area.Solution:

Lateral and total surface area of the cone

Area of Cone

Lateral and total surface area of the cone

Cone has a slant height s which is given as s=h2+r2 (because of Pythagoras theorem).

Here, cone radius (r) =10.52cm=5.25cm and slant height (l) =10cm . Therefore, curved surface area of the cone

  • = (πrl)cm2

  • = (227×5.25×10)cm2

  • = 165cm2

Q-2 Find the total surface area of a cone, if its slant height is 21m and diameter of its base is 24m .Solution:

  • Radius (r) =242m=12m

  • Slant height (l) =21m

Total surface area of the cone

  • πr(l+r)m2

  • 227×12×(21+12)m2

  • (227×12×33)m2

  • 1244.57m2

Q-3 Curved surface area of a cone is 308cm2 and its slant height is 14cm . Find

  1. Radius of the base and

  2. Total surface area of the cone.

Solution:

Solution (I)

Curved surface of a cone =308cm2 and slant height (l) =14cm

Therefore, πrl=308

  • 227×r×14=308

  • r=(308227×14)

  • r=308×722×14

  • r=7cm

Solution (II)

Therefore, total surface area of the cone

  • πr(l+r)cm2

  • 227×7×(14+7)cm2

  • (22×21)cm2

  • 462cm2

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