Surface Area And Volume
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Surface Area And Volume
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25 Questions

1. If the height of a cylinder is increased by 15% and the radius of the base is decreased by 10%, then by what percent will its bended surface region change?
2. If the radius of the base of a cylinder and a cone are in the ratio √3:√2 and their heights are in the ratio of √2:√3. Then their volumes will be in the ratio of:
3. A bakery makes cake in shape of a sector of a circle of radius 10 cm with angle 24∘ at centre and constant thickness 3 cm. Find the volume of raw materials used in making it considering there is no wastage of materials whilke making it.
4. Water is flowing through a pipe of cross sectional radius of 10 cm at the rate of 3 km per hour into a 9 cylinder of radius 5 m and height 2 m. In what time will the cylinder be filled?
5. The total surface range of a cubical box is 600 cm2. The length of longest rod that can be placed in it:
6. If a metallic cone of base radius 30cm and height 45cm is melted and recast into metallic spheres of radius 5cm find the maximum number of spheres that can be made,
7. Thebase of a right prism is a quadrilateral ABCD. If AB=9 cm, BC=14 cm, CD=13 cm, DA=12 cm and ∠DAB=900 and the volume of the prism be 2070 cubic mtr. then the area of the lateral surface of the prism is,
8. A cone and a hemisphere have equal bases and equal volumes. Find the ratio of height cone and radius of hemisphere.
9. A cone and sphere have the same radius of 12 cm. Find the height of the cone if they have equal volume.
10. A cone and sphere have the same radius of 12 cm. Find the height of the cone if they have equal volume.
11. A solid cone of height 9cm and diameter of its base 18cm is cut out from a wooden solid sphere of radius 9cm. The percentage of wood wasted is:
12. Thebase of a right prism is a quadrilateral ABCD. If AB=9 cm, BC=14 cm, CD=13 cm, DA=12 cm and ∠DAB=900 and the volume of the prism be 2070 cubic mtr. then the area of the lateral surface of the prism is,
13. A wooden box measures 20cm by 12cm by 10cm. If thickness of it’s wall is 1cm. Volume of the wood required to make the box (in cubic cm) is,
14. Water flows into a tank which is 200 m long and 150 m wide, through a pipe of cross-section (0.3m x 0.2m) at 20 kmph. In what time will the water level be 8?
15. What part of a rectangular shape pond 8 m long, 16.5 m broad and 4 m deep can be filled from the water of a cylindrical tank of diameter 4 m and length 56 m.?
16. The radius of a cylinder is 10cm and height is 4cm. Find the length adding which either to radius or to height will increase the same volume:
17. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.
18. The measurement of the base of a tube shaped drum is 35dm and its height is 24 dm. It is full of milk. How many of packs each of size 25cm ×22cm× 35 cm can be packed from the drum?
19. If a right circular cone is separated into solids of volumes V1, V2 and V3 by two planes parallel to the base, which also trisect the altitude then V1:V2:V3 is,
20. What part of a rectangular shape pond 8 m long, 16.5 m broad and 4 m deep can be filled from the water of a cylindrical tank of diameter 4 m and length 56 m.?
21. If a right circular cone is separated into solids of volumes V1, V2 and V3 by two planes parallel to the base, which also trisect the altitude then V1:V2:V3 is,
22. If the length of each side of a regular tetrahedron is 12cm, then it’s volume will be:
23. If the surface area of three adjacent surfaces of a cuboid are, p, q and r. Then it’s volume will be:
24. The height of a cone is 30cm. A small plane parallel to its base cuts a small cone at the top of it.If it’s volume is 1/27th of the volume of the cone, what is the height of the smaller cone?
25. If a metallic cone of base radius 30cm and height 45cm is melted and recast into metallic spheres of radius 5cm find the maximum number of spheres that can be made,

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