Most Important Geometry Questions PDF

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1. ABC is a right angled triangle, B being the right angle. Mid-points of BC and AC are respectively B’ and A’. The ratio of the area of the quadrilateral AA’B’B of the area of the triangle ABC is
(a) 1 : 2
(b) 2 : 3
(c) 3 : 4
(d) None of the above

 

Solution :

 

2.A cuboidal water tank has 216 litres of water. Its depth is 1/3 of its length and breadth is 1/2 of 1/3 of the difference of length and height. The length of the tank is
(a) 72 dm
(b) 18 dm
(c) 6 dm
(d) 2 dm

Ans.(b)
Sol. Let l=9x, h=3x, b=x
l×b×h=216×1000
(1 litre = 1000 cm3)
9x×3x×x=216000
27x³=216000
x³=8000
x=20
l=180 cm = 18 dm

3. A wooden box measures 20 cm by 12 cm by 10 cm. Thickness of wood is 1 cm. Volume of wood to make the box (in cube cm) is
(a) 960
(b) 519
(c) 2400
(d) 1120

Ans.(a)
Sol. The external dimensions of the box are
l = 20 cm, b = 12 cm, h = 10 cm
External volume of the box = 20 × 12 × 10 = 2400 cm3
Thickness of the wood = 1 cm
Internal length = 20 – 2 = 18 cm
Internal breadth = 12 – 2 = 10 cm
Internal height = 10 – 2 = 8 cm
Internal volume of the box = 18 × 10 × 8 = 1440 cm3
Volume of the wood = (2400 – 1440) cm3

= 960 cm3

4. Two circles with centres A and B and radius 2 units touch each other externally at ‘C’ A third circle with centre ‘C’ and diameter ‘4’ units meets other two at D and E. Then the area of the quadrilateral ABED is
(a) 2√2 sq. units
(b) 3√3 sq. units
(c) 3√2 sq. units
(d) 2√3 sq. units

Answer :

 

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