Volume and Surface Area Mcqs

A boat having a length 3 m and breadth 2 m is floating on a lake The boat sinks by 1 cm when a man gets on it. The mass of man is :__________?

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A boat having a length 3 m and breadth 2 m is floating on a lake The boat sinks by 1 cm when a man gets on it. The mass of man is :__________?

A. 12 kg
B. 60 kg
C. 72 kg
D. 96 kg
Volume of water displaced = (3 X 2 X 0.01) m3 = 0.06 m3.
Mass of man = Volume of water displaced X Density of water
= (0.06 X 1000) kg = 60 kg.

The areas of the three adjacent faces of a rectangular box which meet in a point are known. The product of these areas is equal to :___________?

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The areas of the three adjacent faces of a rectangular box which meet in a point are known. The product of these areas is equal to :___________?

A. the volume of the box
B. twice the volume of the box
C. the square of the volume of the box
D. the cube root of the volume of the box
Let length = 1, breadth = b and height = h. Then,
Product of areas of 3 adjacent faces = (lb x bh x 1h) = (lbh)2 = (Volume)2.

The edges of a cuboid are in the ratio 1 : 2 : 3 and its sunface area is 88 cm2. The volume of the cuboid is :_________?

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The edges of a cuboid are in the ratio 1 : 2 : 3 and its sunface area is 88 cm2. The volume of the cuboid is :_________?

A. 24 cm3
B. 48 cm3
C. 64 cm3
D. 120 cm3
Let the dimensions of the cuboid be x, 2x and 3x.
Then, 2 (x X 2x + 2x X 3x + x X 3x) = 88
⇔ 2X2 6X2 + 3X2 = 44 ⇔ 11X2 = 44 ⇔ X2 = 4 ⇔ x = 2.
Volume of the Cuboid = (2 X 4 X 6) cm3 = 48 cm3.

A cuboidal, block of 6 cm X 9 cm X 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be_________?

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A cuboidal, block of 6 cm X 9 cm X 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be_________?

A. 6
B. 9
C. 24
D. 30
Volume of block = (6 X 9 X 12) cm3 = 648 cm3.
Side of largest cube = H.C.F. of 6 cm, 9 cm, 12 cm = 3 cm.
Volume of this cube = (3 X 3 X 3) = 27 cm3.
Number of cubes = 648/27 = 24.