Mathematic Worksheet - 12
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4. Right Circular Cone. r-radius, h-vertical height, l-slant height
iii.T.S.A =πr( r+ 1)
iv.l2=r2 + h2
i. Volume =a3
ii. T.S.A = 6a2
iii. Diagonal = a
i.V = 4/3πr3
ii.S.A. or T.S.A. = 4πr2
3.Right Circular Cylinder.
ii. Curved Surface Area or Lateral Surface Area = 2
iii.T.S.A = πr(h+r) = 2
i.V = 2/3 πr3
ii.C.S.A = 2πr2
iii. T.S.A =3πr2
1. If the number of square centimetres on the surface of a sphere is equal to the number of cubic centimetres in its volume, what is the diameter of the sphere?
2. From a solid cylinder whose height is 8 cm and radius is 6 cm, a conical cavity of height 8 cm and base radius 6 cm is hollowed out. Find the volume of remaining solid. ( Take = 22/7)
3. A cylindrical cistern whose radius is 7 cm is partly filled with water. If a conical block of iron whose radius of base is 3.5 cm and height is 6 cm is wholly immersed in the water, by how much will the water level rise? (Take = 22/7 )
4. A solid right circular cone of height 20 cm and base radius 15 cm is melted and casted into smaller cones of equal sizes with height 5 cm and base radius 1.5 cm. Find how many cones are made?
5. A vessel in the form of a cuboid contains some water. If three identical spheres are immersed in water, the level of water is increased by 2 cm. If the area of the base of cuboid is 160 sq.cm. and height is 12 cm, determine the radius of the spheres.
6. A cone of height 15 cm and diameter 7 cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed.
7. A cylinder container is filled with ice-cream, whose diameter is 12 cm and height is 15 cm. The whole icecream is distributed to 10 children in equal cones having hemispherical tops. If the height of conical portion is twice the diameter of its base, find the diameter of the icecream cone.
8. A girl fills a cylindrical bucket 32 cm in height and 18 cm in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, find: a) its radius and b) its slant height. (Leave your answer in square root form).
9. A hollow metallic cylindrical tube has an internal radius of 3 cm and height 21 cm. The thickness of the metal of the tube is ½ cm. The tube is melted and casted into a right circular cone of height 7 cm. Find the radius of the cone correct to one decimal place.
10. From a rectangular solid of metal 42 cm × 30 cm × 22 cm, a conical cavity of base radius 14 cm and height 22 cm is drilled out. Find :
a) the surface area of the remaining solid,
b) the volume of the remaining solid,
c) the weight of the material drilled out if it weighs 7 gm per Cm3.
11. A tent is in the form of a right circular cylinder up to height of 3 m and then becomes a right circular cone with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner surface of the tent at the rate of Rs. 4 per sq.m, if the radius of the base is 14 m.
12. A building is the form of a cylinder surmounted by a hemispherical vaulted dome and contains 41 19/21 m3of air. If the internal diameter of the building is equal to its total height above the floor, find the height of the building. ( Take =22/7 )
1) d = 6 cm
3) 0.5 cm
6)282.33 7) 6 cm
8) a) 36 cm b) 43.26 cm
10)a) 6219.52 b) 23202.67 c) 31.621 kg
11) Rs. 4,136 12)2 m