# A vessel is in the form of a hemisphere mounted on a hollow cylinder. The diameter of the hemisphere is 21 cm and the height of vessel is 25 cm. If the vessel is to be painted at the rate of Rs. 3.5 per cm2, then find the total cost to paint the vessel from outside.

Given.

A vessel is made by mounting hemisphere on cylinder

The radius of the hemisphere is cm = 10.5 cm.

The total height of the cylinder is 25 cm

Rates of painting = 3.5 per cm2

Formula used/Theory.

Curve surface area of Cylinder = 2πrh

Curve surface area of Hemisphere = 2πr2

As we put hemisphere on hollow Cylinder

Area of Vessel is sum of CSA of both hemisphere and cylinder

Area of vessel = CSA of cylinder + CSA of Hemisphere

= 2πrh + 2πr2

= 2πr[h + r]

As height of hemisphere is equal to radius of hemisphere

Then;

Area of vessel = 2 × × 10.5 × [25 + 10.5]

= 2 × × 10.5 × [35.5]

= 2343 cm2

Rates for 1cm2 = Rs.3.5

Rates of 1648.5 cm2 = Rs.3.5 × 2343

= Rs. 8200.5

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