mensuration area volumes Model Questions & Answers, Practice Test for ibps so prelims 2023
ibps so prelims 2023 SYLLABUS WISE SUBJECTS MCQs
Number System
Simplification
Ratio & Proportion
Profit & Loss
Time & Work
Simple Interest & Compound Interest
Mensuration: Area & Volumes
Quadratic Equations
The diameters of two right circular cones are equal. If their slant heights are in the ratio 3 : 2, then what is the ratio of their curved surface areas?
Answer: (a)
Let the radii and slant height of two right circular cones are $r_1 , l_1 and r_2 , l_2$ , respectively.
∴ Ratio of their curved surface areas
= ${πr_1l_1}/{πr_2l_2} = l_1/l_2 (∵ r_1 = r_2)$
= $3/2$ = 3 : 2
The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36m, then what is its radius equal to ?
Answer: (b)
Diameter of a sphere, d = 6 cm
∴ Radius of a sphere, r = $d/2 = 6/2$ = 3 cm
Let the radius of wire be R cm.
Also, given the length of wire, H = 36 m = 3600 cm
According to question
Volume of sphere = Volume of wire
⇒ $4/3 π r^3 = π R^2 H$
⇒ $4/3 × (3)^3 = R^2 × 3600$
⇒ $R^2 = {4 × 3^2}/{3600} = {(6)^2}/{(60)^2}$
∴ R = $6/{60} = 1/{10}$ = 0.1 cm
A circle is inscribed in an equilateral triangle of side of length l. The area of any square inscribed in the circle is
Answer: (d)
Side of equilateral Δ = l
Then,
In radius of circle = $l/{2√3}$
which is diagonal of the square inscribe in the circle
Let, side of square = x
Then,
$x^2 + x^2 = (l/√3)^2$
$2x^2 = l^2/3$
Area of square, $x^2 = l^2/6$
Let the largest possible right circular cone and largest possible sphere be fitted into two cubes of same length. If C and S denote the volume of cone and volume of sphere, respectively. Then, which one of the following is correct?
Answer: (c)
Let the side of cube = a
According to question
Height = a, radius = $a/2$
r = $a/2$ , h = a
Radius of sphere (R) = $a/2$
∴ Volume of cone (C)
= $1/3 πr^2h = 1/3 π(a/2)^2 a ={πa^3}/{12}$ ...(i)
Volume of sphere (S) = $4/3 πR^3 = 4/3 π(a/2)^3$
= ${πa^3}/6$ ...(ii)
On solving eqs. (i) and (ii),
S = 2C
The volume of spheres are proportional to the cubes of their radii. Two spheres of the same material weigh 3.6 kg and 2.7 kg and the radius of the smaller one is 2 cm. If the two were melted down and formed into a single sphere, what would be its radius?
Answer: (d)
1 kg = 1000 $cm^3$
2700 = k.$2^3$
k = ${2700}/8$
6300 = k. $r^3$
$r^3 = {6300}/{k} = {6300}/{2700} = {8/3},$
$r^3 = {56}/{3}$ = , r = 2.6 cm
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