Quantitative Aptitude: Mensuration Questions Set 5

June 4, 2024June 2, 2024 infoalfabanker

A room 10mtr long 4mtr broad and 4mtr high has two windows of 2*1mtr and 3*2mtr. Find the cost of papering the walls with paper 50cm wide at 25paisa per meter?
A) Rs48
B) Rs50
C) Rs52
D) Rs54
E) Rs46

View Answer
Option C
Solution:
Area of walls = 2(10+4)*4 =112
Area of windows = 2+6 = 8
Area to be covered = 112−8= 104mtr
Length of paper = 104/50*100 =208m
Cost = 208*25/100 = 52
A cubical block of 8m*12m*16m is cut into exact number of equal cubes. The least possible number of cubes will be?
A) 9
B) 24
C) 18
D) 30
E) 12

View Answer
Option B
Solution:
H.C.F of 8,12,16 =4
Least number of cubes = 8*12*16/4*4*4 = 24
Find the volume, curved surface area and the total surface area of a hemisphere of radius 21cm?
A) 19404cm³, 2772cm², 4158cm²
B) 4158cm³, 5000cm², 4000cm²
C) 20000cm³, 40000cm²,1000cm²
D) 30000cm³, 2000cm²,5000cm²
E) 40302cm³, 3320cm²,5650cm²

View Answer
Option A
Solution:
The option which gets divided by 11, will be the answer
Method to check – 19404 = add alternate number = 1+4+4 =9
0+9= 9
Find difference = 9-9=0
If difference is either 0 or divisible of 11 then number is divisible of 11.
Ans ¬– A
A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volume of cube is 2744 cubic cm, what is the approximate volume of the cone?
A) 715
B) 719
C) 729
D) 725
E) 710

View Answer
Option B
Solution:
side of cone 3√2744 = 14
Radius of cone = 7
Height = 14
Volume = 1/3 ∏r²h
1/3*22/7*7*7*14 = 718.66= 719
A hollow cylindrical tube is open at both ends is made of iron 4cm thick. If the external diameter be 52cm and the length of the tube be 120cm, find the number of cubic cm of iron in it?approx
A) 72419
B) 72425
C) 72405
D) 72411
E) 72534

View Answer
Option D
Solution:
H = 120 external diameter – 52
External radius = 26
Internal radius = 26-4 =22
Volume of iron = external volume – internal volume
22/7 * 26 * 26 * 120 – 22/7 * 22 * 22 * 120 = 72411
A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is 2cm and the diameter of the base is 4cm. If a right circular cylinder circumscribe the solid, find how much more space will it cover?
A) 4π cm³
B) 2π cm³
C) 16π cm³
D) 8π cm³
E) 8π cm³

View Answer
Option D
Solution:

R of hemisphere =4/2 = 2cm
H of cylinder = 4cm
R of cone = 2cm
V of cylinder – volume of solid =
=π*2²*4 –(2/3 π*2³+1/3*π*2³)
= 16π − 8π
= 8π
The ratio between volumes of a hemisphere and a cone is 1:1. If the cone’s height is equal to its diameter, then find the ratio of diameter of hemisphere and cone ?
A) 2:1
B) 1:1
C) 3:2
D) 2:3

View Answer
Option B
Solution:
let the radius of hemisphere and cone are r1 and r2
H’s volume/c’s volume = 1/1
So [2/3 πr1³]/[1/3 πr2²*2r2] = 1/1
So r1 : r2 = 1 : 2 or D1 : D2 = 1: 1
If the height of a pyramid is 12cm and its base is a square which perimeter is 40cm, then find the volume of pyramid?
A) 300 cm³
B) 200 cm³
C) 400 cm³
D) 500 cm³

View Answer
Option C
Solution:
perimeter of base =40
Side of base = 10
Area of base = 100
Volume = 1/3 * area of base * height
= 1/3 * 100 * 12 = 400cm³
If the perimeter of square, circle, rectangle, are equal. Then whose area is largest?
A) Circle
B) Square
C) Rectangle
D) All are equal

View Answer
Option A
Solution:
when perimeter of these are equal then descending order of area is
Circle >square> rectangle.
So option A is Ans
A rectangular plot of grass is 50m long and 40m broad. From the center of each side a path of 3m wide goes across the center of the opposite side. Find the area of path?
A) 270
B) 280
C) 251
D) 261

View Answer
Option D
Solution:

area of road = 3*50 + 3*40 −3²
= 270 −9=261

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