Volume and Surface Area
Practice Questions - Volume and Surface Area
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Q15) A rectangular field of dimensions 40 m × 15 m. A tank 6 m long, 4 m broad and 3.5 m deep is dug in the field. The mud taken out is spread evenly over the field. By how much is the level of the field raised? 1) 8.33 cm 2) 0.25 cm 3) 25 cm 4) 27.5 m
Volume of mud taken out = 6×4×3.5 = 84 cu m Area of the field on which mud is spread = Area of the field - Area of the tank = 40 × 15 - 6 × 4 = 336 sq m  Hence, option 3. Q16) A right triangle with sides 3 cm, 4 cm and 5 cm is rotated across the side of 4 cm to form a cone. Find the slant height of the resulting cone. 1) 6 cm 2) 8 cm 3) 5 cm 4) 4 cm
Slant height of the resulting cone = Hypotnuse of the triangle = 5 cm. Hence, option 4. Q17) If 5 cm of rain falls on a square ground of side 100 m. Then find the volume of water in the ground. 1) 500 cu m 2) 50 cu m 3) 750 cu m 4) 5000 cu m
Volume = Area×Depth = 100×100×(1/20) = 500 cu m Hence, option 1. Q18) The edge of a cube is 14 cm. Find the toral surface area. 1) 1176 cm2 2) 588 cm2 3) 882 cm2 4) 1323 cm2
Total Surface Area = 6(14)2 = 1176 cm2 Hence, option 1. Q19) Radius of a right circular cone is increased by 10% and height by 30%. Find the percentage change in its volume? 1) 69% 2) 40% 3) 57.3% 4) 85.9%
Volume of a Cone = (1/3)πr2h As, (1/3)π is a constant hence Volume of a Cone varies directly as the square of the radius and directly as the height. So, Let us suppose the initial radius be 1 unit and initial height be 1 unit. Hence, Initial Volume = (1)2×1 = 1 Radius of a right circular cone is increased by 10% and Height is increased by 30%. ∴ Final radius = 1.1 units, Final height = 1.3 units Hence, Final Volume = (1.1)2×(1.3) = 1.573  Hence, option 3. |