mensuration area volumes Model Questions & Answers, Practice Test for ssc chsl tier 1 2023
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Mensuration: Area & Volumes
ABC is an equilateral triangle inscribed in a circle with AB = 5 cm. Let the bisector of the angle A meet BC in X and the circle in Y. What is the value of AX . AY?
Answer: (a)
In ΔABC,
BX = $5/2$ cm, CX = $5/2$ cm
and AX = $√3/2 × 5 = {5√3}/2$ cm
AY and BC are the chord of circle.
∴ AX × XY = BX × XC
⇒ ${5 √3}/2. ∼ XY = 5/2 . 5/2$
⇒ XY = $5/{2√3}$
∴ AX.AY = $({5√3}/2 + 5/{2√3}) × {5√3}/2 = 25 cm^2$
What is the maximum number of circum-circles that a triangle can have ?
Answer: (b)
Option (b) by definition
A hollow cylindrical drum has internal diameter of 30cm and a height of 1 m. What is the maximum number of cylindrical boxes of diameter 10 cm and height 10 cm each that can be packed in the drum ?
Answer: (d)
Number of cylindrical boxes that can be packed in the drum
= ${π × (15)^2 × 100}/{π × (5)^2 × 10}$ = 90
So, option (d) is correct.
If two lines AB and CD intersect at O such that ∠AOC = 5 ∠AOD, then the four angles at O are
Answer: (c)
Let two lines AB and CD intersect each other as shown in the fig. such that
∠AOD = x
Then, ∠AOC = 5x
Now, ∠AOD + ∠AOC = ∠COD = 180°
x + 5x = 180°
6x = 180° ⇒ x = 30°
Now, ∠AOD = ∠BOC = x = 30°
and ∠AOC = ∠BOD = 5x = 150°
Consider the following statements
I. The opposite angles of a cyclic quadrilateral are supplementary.
II. Angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Which one of the following is correct in respect of the above statements?
Answer: (d)
I. It is true that opposite angles of a cyclic quadrilateral are supplementary.
II. It is also true that the angle subtend by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Hence, both statements are individually true but neither statements implies of each other.
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