Question 1. Find the volume of a right circular cone formed by joining the edges of a sector of a circle of radius r cm where the sector angle makes 90 degree.

Question 2. A rectangular sheet of iron foil is 44 cm long and 20 cm wide. A cylinder is made out of it by rolling the foil once along the width. Find the volume of the cylinder ?

Question 3. A sector of a circle of radius 12 cm has an angle of 120 degree. If it is made into a cone, find the volume of the cone ?

Question 4. A rectangular plot has an area of 490 square meter. If the length of the rectangular plot is 24.5 meter, then find the perimeter of the rectangular plot ?

Question 5. A right circular cone has a height of 6 cm . If two cuts, parallel to the base, are made at height of 1 cm and 3 cm from the base, find the ratio of the volumes of the three parts from the top to the bottom ?

Question 6. There is a large room of size 24 ft x 32 ft. The floor of the room is to be paved with square tiles of the same dimension. Find out the minimum number of tiles required and its size.

Question 7. There is a rectangular field having dimensions 20 meter x 30 meter. There is a jogging track inside the field along its perimeter. The width of the track is uniform and it is equal to 2 meter. Find the total perimeter of the jogging track and the area of the jogging track.

Question 8. If the length of the rectangle is increased by 100 percent and width is increased by 200 percent, what is the percentage increase in the area of the rectangle ?

Question 9. If the area of the square is 3 root 3 times the area of an equilateral triangle, then find the ratio of the sides of the square to the side of the equilateral triangle ?

Question 10. Two cylindrical jars have their diameter in the ratio 2:3 and their heights are in the ratio 3:2. Find the ratio of their volumes ?

Question 11. A horse is tied with a rope of length 7 meter at one corner of square field having one side equal to 10 meter. Find the minimum possible area of the square field that is left ungrazed.

Question 12. A field is in the form of a rectangle having length 20 meter and breadth 15 meter. There is a square pit having dimension 15 meter x 15 meter. The pit is to be filled uniformly upto a height of 4 meter by the soil taken out by digging the rectangular field. Find out the depth upto which the rectangular field must be dug if the soil is taken out uniformly.

Question 13. A spherical copper ball, whose diameter is 14 cm, is melted and converted into a wire having diameter equal to 14 cm. Find the length of the wire.

Question 14. A metallic cone of diameter 32 cm and height 9 cm is melted and made into identical spheres each of radius 2 cm. How many such spheres can be made ?

Question 15. The interior of a building is in the form of a cylinder of diameter 6 meter, surmounted by a cone of vertical angle 60 degree and having an overall height 12 root 3 meter. Find the volume of the building ?

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