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Answer :

Let the diameter of a sphere be d.

After decreasing, diameter of the sphere

= d – \(\frac{25}{100} \) x d

= d –\(\frac{1}{4} d = \frac{3}{4} d \)

Since, surface area of a sphere

= \( 4\pi r^2 \)

= \( \pi (2r)^2 \)

= \( \pi d^2 \)

Surface area of a sphere, when diameter of the sphere is

= \(\pi (\frac{3}{4} d)^2 \)

= \(\pi \frac{9}{16} d^2 \)

Now, decrease percentage in curved surface area

= \(\frac{\pi d^2 - \pi \frac{9}{16} d^2 }{\pi d^2} × 100 \)

= \(\frac{16-9}{16} × 100 \)

= \( \frac{7}{16} × 100 \)

= 43.75%

- Height = 110cm, Depth = 25cm, Breadth = 85cm (see figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing-is 20 paise per \(cm^2 \)and the rate of pointing is 10 paise per \(cm^2 \) find the total expenses required for palishing and painting the surface of the bookshelf.
- The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in figure. Eight such spheres are-used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per \( cm^2 \) and black paint costs 5 paise per \( cm^2 \).

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