Question 1 :
A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 4989.60. If the cost of white-washing is Rs 20 per square metre, find the inside surface area of the dome.

Question 2 :
A conical tent is 10 m high and the radius of its base is 24 m. Find the cost of the canvas required to make the tent, if the cost of 1 $m^2$ canvas is Rs 70.

Question 3 :
The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.

Question 4 :
The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.

Question 5 :
Find the surface area of a sphere of radius 14 cm.

Question 6 :
It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per $m^2$ , find the capacity of the vessel.

Question 7 :
State true or false: If the length of the diagonal of a cube is $6\sqrt3$ cm, then the length of the edge of the cube is 3 cm.

Question 9 :
Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions $4m\times3m$?

Question 10 :
Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.

Question 11 :
A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 4989.60. If the cost of white-washing is Rs 20 per square metre, find the volume of the air inside the dome.

Question 12 :
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. Which box has the greater lateral surface area and by how much?

Question 13 :
The diameter of a sphere is decreased by $25\%$. By what per cent does its curved surface area decrease?

Question 14 :
What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use $\pi$= 3.14).

Question 15 :
A godown measures 40 m × 25 m × 15 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.

Question 16 :
The height of a cone is 15 cm. If its volume is 1570 $cm^3$ , find the radius of the base. (Use $\pi$ = 3.14)

Question 17 :
A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

Question 18 :
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per $m^2$ .

Question 19 :
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

Question 20 :
Find the surface area of a sphere of diameter 3.5 m.