Q17 of 48 Page 1

The diameter of a sphere is decreased by 25%. By what percent does its curved surface area decrease?

Concept Used: Curved Surface Area of Sphere = 4πr2


Radius


Given: Diameter of the Sphere is decreased by 25%


Assumption:


Let r1 be the initial radius, r2 be the increased radius


Explanation:


Radius (r1)


New radius (r2)



Initial Surface Area = CSA (S1) = 4πr12



= πd2


Decreased Surface Area = CSA (S2) = 4πr22




Decrease in surface area = S1 – S2




Now,


Percentage decrease




= 43.75 %


Hence, the decrease in surface area is 43.75%.


More from this chapter

All 48 →
14

A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm, and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

 16

A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius of 4 cm. Find the height and slant height of the cone.

 18

The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find

(i) The height of the cone


(ii) The slant height of the cone


(iii) The curved surface area of the cone

 19

A conical heap is formed when a farmer pours food grains on a ground. The slant height of the heap is 35 cm. The circumference of the base is 132 cm. What amount of tarpaulin is needed to cover the grains? Farmer goes to the orphanage and gives half of the food grains for the children living there. How many grains farmer donated?