Question

students of class 12 presented a gift to their school in the form of an electric lamp in the shape of a glass hemispherical base surmounted by a metallic cylindrical top of same radius 21 cm and height 3.5 cm. the top was silver coated and the glass surface was painted red. what is the cost of silver coating the top at the rate ₹5 per 100 cm2? what is the surface area of the glass to be painted red?​

Answer 1

Step-by-step explanation:

Cost of painting silver is ₹92.4

And area to be painted red is 2772cm2

Answer 2

Cost of silver coating the top is  Rs 92.40 and Surface area of glass to be painted red is 2772 cm².

Explanation:

Radius of cylindrical top $=21cm$ ; $r=21cm$

Height of cylindrical top $=3.5cm$ ; $h=3.5cm$

The area which has to be coated silver is curved surface area of cylindrical top + upper of cylinder

Curved surface area of cylinder = $2\pi rh$

So, area to be coated silver = $2\pi rh+\pi r^{2}$

                                       $=$ $2\times\dfrac{22}{7}\times21\times3.5+\dfrac{22}{7}\times21^2$

                                              = $1848cm^{2}$

Cost of coating $100cm^{2} =$ Rs $5$

Cost of coating $1 cm^{2}$ $=$ Rs $\frac{5}{100}$                     (using unitary method)

Cost of coating $1848 cm^{2} =$  $\frac{5}{100}\times1848$

                                      $=$ Rs $92.40$

Area of glass to be painted red is curved surface area of hemisphere

Radius of hemisphere $=21cm$ ; $r=21cm$

Curved Surface area of hemisphere $=2\pi r^{2}$

So, surface area of glass to be painted $=2$×$\frac{22}{7}$×$21$×

                                                                 $=2772cm^{2}$

                                 

# Learn more :

The volume of a cylinder is 225 cm and its height is 9 cm.

What is the length of the cylinder's radius?

9cm

10cm

7cm

5cm

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