While Preparing for Geometry and Mensuration section, questions on Area and Volume are asked frequently. Here the concepts and formulas should be understood well.
We have provided the selective and important Area and Volume questions and answers for various Aptitude tests and competitive exams. Try to solve maximum Area and Volume questions to increase your performance in exams.
Q1) An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
A) 4%
B) 2%
C) 4.04%
D) 2.02%
Solution :
Q2) A towel, when bleached, lost 20% of its length and 10% of its breadth. What is the percentage decrease in area?
A) 26%
B) 28%
C) 30%
D) 32%
Solution :
Q3) If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area?
A) 50% increase
B) 25% increase
C) 25% decrease
D) 50% decrease
Solution :
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Q4) A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 square feet, how many feet of fencing will be required?
A) 82
B) 92
C) 95
D) 88
Solution :
Q5) A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
A) 720
B) 900
C) 1200
D)1800
Solution:
2(15 + 12) x h = 2(15 x 12)
h =180/27m =20/3m.
Volume = (15 x 12 x 20/3) m3= 1200 m3
Q6) A cylindrical jar of radius 15 cm is filled with water up to a height of 25 cm. 15 spherical balls of radii 2 cm each are immersed in the jar. Find the new level to which water is filled in the jar. [Take π = 3.]
A) 25.71 cm
B) 32.71 cm
C) 27.71 cm
D) 30.71 cm
Solution:
Volume of one sphere = 4 / 3× 3 × (23) = 32 cm3
[Volume of the sphere = 4 / 3π (r3).]
Volume of 15 spheres = 15 × 32 = 480 cm3
[Multiply.]
Volume of water in the jar = 3 × (152) × 25 = 16875 cm3
[Volume of the cylinder = π (r2) h.]
Total volume of water + balls(V) ⇒ 480 + 16875 = 17355 cm3
[Simplify.]
Volume of the water in the cylinder when spherical balls are immersed = 17355 cm3
⇒ 3 × (15)2 h = 17355 cm3
Height to which water is filled in the jar ⇒ 173553 × (15)² = 25.71 cm
Q7) 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
A) 20 cm
B) 25 cm
C) 35 cm
D) 50 cm
Solution:
Total volume of water displaced = (4 x 50) m3 = 200 m3
Rise in water level = (200/40 x 20) m 0.25 m = 25 cm
Q8) A cube of edge 15 cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of the vessel are 20 cm × 15 cm, find the rise in water level.
A) 10.25 cm
B) 11.25 cm
C) 12.25 cm
D)13.25 cm
Solution:
Increase in volume = Volume of the cube = (15 × 15 × 15) cm³
Raise in water level = (Volume/Area) = (15 x 15 x 15/ 20 x 15)cm = 11.25 cm
Q9. The side of a cube is 15 m, find it's surface area?
A) 1350 m2
B) 1250 m2
C) 1300 m2
D) 1450 m2
Solution:
Surface area = 6 a2 sq. units
6 a2 = 6 × 225 = 1350 m2
Q10) The volume of a cube is 1728 cc. Find its surface.
A) 864 Sq.cm
B) 648 Sq.cm
C) 486 Sq.cm
D) 468 Sq.cm
Solution:
a3 = 1728 => a = 12
6a2 = 6 * 12 * 12 = 864 Sq.cm
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