Surface Area and Volume (hots) question class-Xth

Surface Area and Volume Questions

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1.The diameter of a metallic sphere is 6cm. It is melted and drawn into a wire having diameter of the cross-section as 0.2cm. Find the length of the wire.

2. The diameter of a metallic sphere is 6cm. The sphere is melted and drawn into a wire of uniform cross-section .If the length of the wire is 36m ,find it's radius.

3. If the diameter of cross-section of wire is decreased by 5% how much percent will the length be increased so that the volume remains the same?

4. A sphere of diameter 6cm is dropped in right circular cylindrical vessel partly filled with water .The diameter of the cylindrical vessel is 12cm .If the sphere is completely submerged in water, by how much will the level of a water rise in the cylindrical vessel?

5. A 20m deep well with diameter 7m is dug and the earth from digging is evenly spread out to form a platform 22m by 14m .Find the height of the platform.

6. A cylindrical pipe has inner diameter of 7cm and water flows through it at 192.5 litres per minute .Find the rate of flow in kilometres per hour .

7. Water is flowing at the rate of 3km/hr through a circular pipe of 20cm internal diameter into a circular cistern of diameter 10m and depth 2m. In how much time will the cistern be filled?

8. Water is flowing through the rate of  7 metres per second through a circular pipe whose internal diameter is 2cm into a cylindrical tank the radius of whose base is 40cm. Determine the increase in water level in 1/2 hour .

9. The rain water from a roof of 22m × 20m drains into a cylindrical vessel having diameter of base 2m and height 3.5m .If the vessel is just full , find the rainfall in cm.

10. Water in a canal, 30dm wide and 12dm deep is flowing with velocity of 10km/hr . How much area will it irrigate in 30 minutes ,if 8cm of standing water is required for irrigation?

11. An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone .The radius of the base of each of cone and cylinder is 8cm. The cylindrical part is 240cm high and the conical part is 36cm high. Find the weight of the pillar if one cubic cm of iron weighs 7.8 grams.

12. A circus tent is cylindrical upto a height of 3m and conical above it. If the diameter ok of the base is 105m and the slant height of the conical part is 53m , find the total canvas used in making the tent.

13. A right circular cylinder having diameter 12cm and height 15cm is full of ice-cream. The ice cream is to be filled in cones of height 12cm and diameter 6cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

14. A tent is of the shape of a right circular cylinder upto a height of 3 metres and then becomes a right circular cone with a maximum height of 13.5 metres above the ground. Calculate the cost of painting  the inner side of the the tent at the rate of Rs 2per square metres.

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15. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere . If the radius of the hemisphere is 4.2cm and the total height of the toy is 10.2cm , find the value of the wooden toy.

16. A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The whore icecream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice cream cone.

17. A solid is in the form of cylinder with hemispherical ends. The total height of the solid is 19 cm and diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid. (Use π =22/7)

18. A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder.the diameter of the sphere is 14 cm and the height of the vessel is 13 cm. Find its capacity. (Take π=22/7)

19. A solid toy is in the form of right circular cylinder with hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and height of the cylinder cylinderical and conical portion are 12 cm and 7 cm respectively. Find the volume of the solid toy. Take π=22/7.

20. From a solid circular cylinder with height 10 cm and radius of base 6cm,a right circular cone of the same height and the same base is removed. Find the volume of the remaining solid. Also find the whole surface area.

21. A golf ball has diameter equal to 4.1 cm. Its surface has 150 dimples each of radius 2 cm . Calculate the total surface area which is exposed to the surrounding assuming that the dimples are hemispherical.

22. A cone made of paper has height 3h and vertical angle 2alpha. It contains two other cones of height 2h and h and vertical angles 4 alpha and 6 alpha respectively. Find the ratio of the two volume in between the cones.

23. A hemispherical depression is cut out from one face of the cubical wooden block such that the diameter of l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

24. A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of it's ends. The length of the entire capsule is 14 mm and a diameter of the capsule is 5mm. Find its surface area.

25. A juice seller was serving his customers using glasses. The inner diameter of the cylinder class 5 cm,but the bottom of the glass had a hemispherical raised portion which reduce the capacity of the glass. If the height of the glass was 10 cm, find what so what the apparent capacity of the glass was and what the actual capacity was.

 ( Use π= 3.14)

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By Anuranjan Gadekar

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