1

Question

The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given 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}.

Open in App

Solution

In the given problem, we have 8 spheres mounted upon small cylindrical supports, as shown in the diagram.

Now, the spheres are to be painted silver. So, let us first find the surface area of the spheres first.

Diameter of the sphere = 21 cm

So, radius of the sphere = 10.5 cm

Now,

This is the surface area of one sphere. We have 8 such spheres. So,

Total surface area of 8 spheres =

cm^{2}

At the junction of the sphere and the cylinder, there is some portion which would be covered. Hence, that would not be painted silver.

The covered area

So, for 8 spheres,

The covered area

Therefore, the total area to be painted

Now, the rate of silver paint per cm^{2} = 25 paisa

=Rs 0.25

So, the cost of silver paint for 8 spheres =

= Rs 2757.86

Now, the cylinders are to be painted black. So, let us find the surface area of the cylinders.

Radius of the cylinder = 1.5 cm

Height of the cylinder = 7 cm

Now,

This is the surface area of one cylinder. We have 8 such cylinders. So,

Total surface area of 8 cylinder =

cm^{2}

Now, the rate of black paint per cm^{2} = 5 paise

= Rs 0.05

So, the cost of silver paint for 8 cylinders =

Therefore,

The total cost of the paint = cost of silver paint + cost of black paint

Therefore, the cost of painting would be

1

View More

Join BYJU'S Learning Program

Join BYJU'S Learning Program