The radii of the bases of a cylinder and a cone are in the of 3 : 4 and their heights are in the ratio 2 : 3. Find the ratio of their volumes:
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Solution
Ratio of volumes = = 9 : 8
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes:
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Solution
Let r be the radius of each
Height of hemisphere = radius
∴ Height of each = r
Ratio of volumes =
= 1 : 2 : 3
A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire:
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Solution
Length of wire = = 24300 cm
= 243 m
What approximate value should come in place of the question mark (?) in the following question?
424.99 × 23.94 ÷ 8.054 = ?
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Solution
424.99 × 23.94 ÷ 8.054 ≈ 425 × = 1275
What approximate value should come in place of the question mark (?) in the following question?
25.05% of 2845 + 14.95 × 2400 = ?
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Solution
What approximate value should come in place of the question mark (?) in the following question?
4005.33 ÷ 19.89 × 1.9 = ?
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Solution
4005.33 ÷ 19.89 × 1.9 ≈
What approximate value should come in place of the question mark (?) in the following question?
16.002 × 14.897 × 20.39 = ?
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Solution
16.002 × 14.897 × 20.39 ≈ 16 × 15 × 20 = 4800
The area of a rhombus is 150 cm2. The length of one of its diagonals is 10 cm. The length of the other diagonal is:
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Solution
second diagonal = 150
∴ second diagonal = = 30 cm
If the radius of a circle is doubled, its area is increased by:
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Solution
% increase = 100 + 100 +
The circumference of a circle is 100 cm. The side of a square inscribed in the circle is:
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Solution
2πr = 100
r =
Diameter of circle = Diagonal of square
= (side)
∴ Side = cm