mensuration area volumes Model Questions & Answers, Practice Test for ssc mts paper 1 2023
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In the figure given above, if ∠AOP = 75° and ∠AOB = 120°, then what is the value of ∠AQP?
Answer: (c)
∠AQP = $1/2 × ∠AOP = {75°}/2$ = 37.5°
The outer and inner diameters of a circular pipe are 6 cm and 4 cm, respectively. If its length is 10 cm, then what is the total surface area in sq cm?
Answer: (c)
Given, R = 3 cm, r = 2 cm, h = 10 cm
Total surface area = 2πRh + 2πrh + 2π ($R^2 – r^2$)
= 60π + 40π + 10π
= 110π sq cm
The distance between the centres of two circles having radii 4.5 cm and 3.5 cm respectively is 10 cm. What is the length of the transverse common tangent of these circles?
Answer: (a)
Length of common tangent,
= $√{d^2 - (r_1 + r_2)^2}$
= $√{10^2 - (4.5 + 3.5)^2}$
= $√{100 - 64} = √{36}$
= 6 cm
What is the whole surface area of a cone of base radius 7 cm and height 24 cm?
Answer: (c)
Slant height, l = $√{h^2 + r^2}$
= $√{(24)^2 + (7)^2} = √{576 + 49} = √{625} = 25$
Total surface area = πrl + π $r^2$
= ${22}/7 × 7 × 25 + {22}/7 × 7 × 7$ = 704 sq cm.
Six cubes, each with 12 cm edge are joined end to end. What is the surface area of resulting cuboid?
Answer: (a)
Resulting surface area of cuboid
= 2(l × b + b × h + l × h)
= 2(12 × 72 + 12 × 12 + 72 × 12)
= 2(864 + 144 + 864)$cm^2$
= 2 × 1872 $cm^2$
= 3744 $cm^2$
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