Quantitative Aptitude: Mensuration Questions Set 14

1. The perimeter of an equilateral triangle is equal to the perimeter of a square whose diagonal is 9√2 cm. Find out the area of the equilateral triangle ?
   48√3
   60√3
   30√3
   36√3
   20√3
   Option D
   side of square=9√2/√2=9
   let the side of equilateral triangle be x cm.
   3x=4*9
   x=12
   area of equilateral triangle= √3/4*12*12=36√3
   
    



2. If ratio of height and radius of a cone is 5:6. Volume of cone is 480π cm^3, then find slant height of cone (in cm) ?
   2√61
   4√61
   8√50
   9√68
   10√52
   Option A
   let height and radius of cone be 5x and 6x.
   volume of cone =480π
   1/3*π*6x^2*5x=480π
   x^3=8
   x=2 cm
   height=10cm , radius=12 cm
   so, slant height of cone =√(r^2+h^2)
   = √(144+100)=√244=2√61
   
    



3. Circumference of a circle A is 2 times perimeter of a square. Area of the square is 484 cm^2. What is the area of another circle B whose radius is half the radius of the circle A ?
   530
   640
   590
   616
   none of these
   Option D
   Area of the square =484cm
   side of square =22cm.
   perimeter of square =22*4=88cm.
   ATQ,
   circumference of a circle A=88*2 =176cm.
   2πr =176
   r=176*7/44 =28
   Radius of circle B= 28/2 =14cm.
   Area of circle B=22/7*14*14 =616cm^2
   
    



4. If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 288 m^2 . What is the area of the original rectangle ?
   400
   300
   520
   220
   none of these
   Option B
   Percentage change in area =
   +20-20-(20*20)/100 =-4%
   96%= 288
   100%=288/96*100= 300 m^2
   
    



5. Side of a rhombus is 20cm and the ratio of diagonals of a rhombus is 3:4, then find the area of the rhombus .
   384
   264
   544
   288
   484
   Option A
   Side of rhombus =20cm.
   Let,
   two diagonals of a rhombus be 3x and 4x.
   side =√(3x)^2+(4x)^2
   = 9x^2+16x^2 =5x
   5x=20
   x=4
   two diagonals =(4*3*2) and (4*4*2) =24 and 32
   Area =1/2*24*32 =384 cm^2.
   
    



6. The side of a square is 20% more than the side of an equilateral triangle whose perimeter is 75m. Find the ratio between perimeter of square to area of triangle.
   96:125√3
   48:55√3
   32:58
   96:130√3
   32:42
   Option A
   perimeter of triangle=75
   side of triangle=75/3=25m
   side of square=25*120/100=30 m
   perimeter of square=4*30=120 m
   area of triangle=√3/4*25*25=625√3/4 m^2
   ratio=120:625√3/4=480:625√3=96:125√3
   
   
    



7. Radius of circular field is 40% more than length of a rectangular field, having the area 80 m^2. If circumference of a circle is 88m, then radius of circular field is what percent more than breadth of rectangular field ?
   60
   50
   120
   75
   100
   Option D
   let radius of circle =7x
   and length of rectangular field=10m
   area of rectangular field=80 m^2
   10*breadth=80
   breadth=8m
   required percentage=14-8?8*100=6/8*100=75%
   
    



8. Perimeter of a circle is 88cm. Find volume of a cylindrical vessel whose radius is equal to the radius of circle and height of cylindrical vessel is 20 cm.
   15000
   12320
   14220
   16780
   20400
   Option B
   Perimeter of circle =88
   r=88*7/44=14 cm
   radius of cylindrical vessel =22/7*14*14*20 = 12320 cm^2
   
    



9. The ratio between length and breadth of a rectangular field is 5:4 . If area of rectangular field is 320 m^2, then find the perimeter of rectangular field.
   64
   40
   100
   72
   84
   Option D
   Let length of field =5x
   breadth of field =4x
   ATQ,
   5x*4x =320
   20x^2=320
   x^2 =320/20 =16
   x=4
   Perimeter =2(5x+4x) =18x =18*4= 72
   
    



10. The total area of a circle and a square is equal to 1241 cm^2. The diameter of the circle is 28cm. What is the sum of the circumference of the circle and the perimeter of the square ?
    132
    188
    192
    288
    196
    Option B
    diameter of circle=28cm
    radius=14cm
    area of circle=22/7*14*14=616
    ATQ,πr^2+a^2=1241
    a^2=1241-616=625
    a=25
    circumference of the circle=2*22/7*14=88
    perimeter of square=4a=4*25=100
    sum=88+100=188
    
     

 

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