HARD
10th Foundation
IMPORTANT
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The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base is the section made?

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Important Questions on Surface Areas and Volumes

MEDIUM
10th Foundation
IMPORTANT
IMO Olympiad Work Book 10>Chapter 13 - Surface Areas and Volumes>MATHEMATICAL REASONING>Q 9
A cuboidal metal of dimensions 44 cm×30 cm×15 cm was melted and cast into a cylinder of height 28 cm. Its radius is 
MEDIUM
10th Foundation
IMPORTANT
IMO Olympiad Work Book 10>Chapter 13 - Surface Areas and Volumes>MATHEMATICAL REASONING>Q 10
Study the question and the statements given below and decide which of the statement(s) is/are necessary to answer the question.
What is the capacity of the cylindrical tank?
I. The area of the base is  61,600 sq.cm.
II. The height of the tank is 1.5 times the radius.
Ill. The circumference of base is 880 cm.
HARD
10th Foundation
IMPORTANT
IMO Olympiad Work Book 10>Chapter 13 - Surface Areas and Volumes>MATHEMATICAL REASONING>Q 11
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed into the tub. If the radius of the hemisphere is 3.5 cm and the height of the cone outside the hemisphere is 5 cm, find the volume of water left in the tub. (Take π=22/7)
EASY
10th Foundation
IMPORTANT
IMO Olympiad Work Book 10>Chapter 13 - Surface Areas and Volumes>MATHEMATICAL REASONING>Q 12
Find the maximum Volume of a Cone that can be carved out of a solid Hemisphere of radius r.
MEDIUM
10th Foundation
IMPORTANT
IMO Olympiad Work Book 10>Chapter 13 - Surface Areas and Volumes>MATHEMATICAL REASONING>Q 13
A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The rise in water level is 0.8 cm. The diameter of each ball is 
MEDIUM
10th Foundation
IMPORTANT
IMO Olympiad Work Book 10>Chapter 13 - Surface Areas and Volumes>EVERYDAY MATHEMATICS>Q 14
The internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm respectively. The cost to paint 1 cm2 of the surface is ₹ 0.05. Find the total cost to painting the vessel all over.
MEDIUM
10th Foundation
IMPORTANT
IMO Olympiad Work Book 10>Chapter 13 - Surface Areas and Volumes>EVERYDAY MATHEMATICS>Q 15
A bucket is in the form of a frustum of a cone, its depth is 15 cm  and the diameters of the top and the bottom are 56 cmand 42 cm respectively. How many litres can the bucket hold?
MEDIUM
10th Foundation
IMPORTANT
IMO Olympiad Work Book 10>Chapter 13 - Surface Areas and Volumes>EVERYDAY MATHEMATICS>Q 16
To construct a wall 24 m long, 0.4 m thick and 6 m high, bricks of dimensions 25 cm×16 cm×10 cm each are used. If the mortar occupies 110th of the volume of the wall, find the number of bricks used.