NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.9 – Part 2

Curved surface area, total surface are and volumes of common solids

Curved Surface Area, Total Surface Are and Volumes

Curved surface area, total surface are and volumes of common solids

Q-2 The front compound wall of a house is decorated by wooden spheres of diameter Equation place on small supports as shown in the figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius Equation and height Equation and is to be painted black. Find the costs if silver paint costs Equation paise per Equation and black paint costs Equation paise per Equation .

Front compound wall of house,give it diameter 21cm,radius=1.5cm,height=7cm

Front Compound Wall of House

Front compound wall of house,give it diameter 21cm,radius=1.5cm,height=7cm

Solution:

Given,

  • Compound wall of a house is decorated by wooden spheres of diameter Equation .

  • Cylinder has radius Equation

  • Height of cylinder Equation

  • Cost of black paint (for spheres) is Equation paise per Equation

  • Cost of silver paint (for cylinder) is 2 Equation paise per Equation

Surface area to be silver painted Equation (curved surface area of the sphere - area of circle on which sphere is resting)

  • Equation

  • Equation ( Equation )

  • Equation

  • Equation

  • Equation

Cost of silver paint Equation paise per Equation , therefore total cost of silver painting,

  • Equation

  • Equation

  • Equation (approx.)

Surface area to be black painted Equation curved area of cylinder. (since there are 8 cyliners)

  • Equation

  • Equation

  • Equation

Cost of black paint Equation paise per Equation . Therefore total cost of black painting,

  • Equation

  • Equation

Therefore, total cost of painting Equation = Equation (approx.)

Q-3 The diameter of a sphere is decreased by Equation By what percent does its curved surface area decrease?

Solution:

Let d be the diameter of the circle,

Its surface area = Equation , since Equation . Therefore, surface area = Equation Equation

On decreasing its diameter by Equation , the new diameter becomes, Equation

Therefore, surface area Equation

Therefore decrease in surface area between two spheres = Equation

  • Equation

  • Equation

Therefore percentage decrease in surface area Equation

  • Equation

  • Equation

  • Equation

  • Equation

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