Q3 of 48 Page 261

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


More from this chapter

All 48 →
1

A toy is made by mounting a cone onto a hemisphere. The radius of the cone and a hemisphere is 5 cm. The total height of the toy is 17 cm. Find the total surface area of the toy.

 2

A show - piece shown in figure 14.10 is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 7 cm and the hemisphere fixed on the top has diameter 5.2 cm. Find the total surface area of the piece.

 4

Chirag made a bird - bath for his garden in the shape of a cylinder with a hemispherical depression at one end, (see the figure 14.11). The height of the cylinder is 1.5 m and its radius is 50 cm. Find the total area of the bird - bath. (π = 3.14)

 5

A solid is composed of a cylinder with hemispherical ends on both the sides. The radius and the height of the cylinder are 20 cm and 35 cm respectively. Find the total surface area of the solid.