Aptitude Questions: Mensuration Set 7

Hello Aspirants. Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample from Mensuration that are important for all the competitive exams. We have included some questions that are repeatedly asked in exams !!

1. The length and the breadth of a rectangular door are increased by 1 m each and due to this the area of the door increased by 21 sq. m. But if the length is increased by 1 m and breadth decreased by 1 m, area is decreased by 5 sq. m. Find the perimeter of the door.
   A) 25 m
   B) 20 m
   C) 40 m
   D) 60 m
   E) 24 m
   
   Answer & Explanation

   C) 40 m
   Explanation:
   Let original length = l, breadth = b, so area = lb
   When l and b increased by 1:
   (l+1)(b+1) = lb + 21
   Solve, l + b = 20
   When l increased by 1, b decreased by 1:
   (l+1)(b-1) = lb – 5
   Solve, l – b = 6
   Now solve both equations, l = 13, b = 7
   Perimeter = 2(13+7)
   
   
   
2. The perimeter of a rectangular plot is 340 m. Find the cost of gardening 1 m broad boundary around it at the rate of Rs 10 per sq. m.
   A) Rs 3450
   B) Rs 3400
   C) Rs 3480
   D) Rs 3440
   E) Rs 3880
   
   Answer & Explanation

   D) Rs 3440
   Explanation:
   Given 2(l+b) = 340
   1 m broad boundary means increase in l and b by 2 m
   So area of the boundary will be [(l+2)(b+2) – lb] = 2(l+b) + 4 = 340 + 4 = 344
   So cost of gardening = 344*10
   
   
   
3. The sides of a triangle are in the ratio 3 : 4 : 5 whose area is 216 sq. cm. What will be the perimeter of this triangle?
   A) 58 cm
   B) 64 cm
   C) 28 cm
   D) 36 cm
   E) 72 cm
   
   Answer & Explanation

   E) 72 cm
   Explanation:
   Sides 3x, 4x, 5x
   So semi-perimeter, s = (3x+4x+5x)/2 = 6x
   Area = √s(s-a)(s-b)(s-c)
   = √6x*3x*2x*x = 6x² cm²
   So 6x² = 216, this gives x = 6
   Perimeter = 12x = 12*6
   
   
   
4. If the base of a triangle is increased by 50% and its height is decreased by 50%, then what will be the effect on its area?
   A) 50% decrease
   B) 75% increase
   C) No effect
   D) 25% decrease
   E) 25% increase
   
   Answer & Explanation

   D) 25% decrease
   Explanation:
   Area of triangle = (1/2) * base * height
   So effect on area = +50 + (-50) + (50)(-50)/100 = -25%
   
   
   
5. A rectangle whose sides are in the ratio 6 : 5 is formed by bending a circular wire of radius 42 cm. Find the largest side of the rectangle.
   A) 60 cm
   B) 72 cm
   C) 66 cm
   D) 78 cm
   E) 84 cm
   
   Answer & Explanation

   B) 72 cm
   Explanation:
   Length of wire = 2ᴨr = 264 which should be equal to the perimeter of rectangle in which it is bent.
   So 2(6x + 5x) = 264
   Solve, x= 12
   Largest side = 6x = 6*12
   
   
   
6. A rectangular sheet of 0.5 cm thickness is made from an iron cube of side 10 cm by hammering it down. The sides of the sheet are in the ratio 1 : 5. Find the largest side of the sheet.
   A) 100 cm
   B) 72 cm
   C) 20 cm
   D) 70 cm
   E) 88 cm
   
   Answer & Explanation

   A) 100 cm
   Explanation:
   Sides = x and 5x
   Now vol. of rectangle = vol. of cube
   x * 5x * (0.5) = 10*10 *10
   Solve, x = 20
   Largest side = 5x = 5*20
   
   
   
7. The area of the inner part of a cylinder is 616 sq. cms and its radius is half its height. Find the inner volume of the cylinder.
   A) 1577.5 cm³
   B) 1768.2 cm³
   C) 1538.5 cm³
   D) 1435.8 cm³
   E) 1238.5 cm³
   
   Answer & Explanation

   B) 1538.5 cm³
   Explanation:
   Given 2ᴨrh + ᴨr² = 616 and r = (1/2) * h
   So 2ᴨ × (1/2)h × h + ᴨ × (1/4)h² = 616
   Solve, h = 28/√5
   Volume = ᴨr²h = (22/7) * (1/4) * h² * h
   Put h = 28/√5, vol. ≈ 1538.5
   
   
   
8. A cylinder and a cone have equal base and equal height. The ratio of the radius of base to height is 5 : 12. Find the ratio of the total surface area of the cylinder to that of the cone.
   A) 7 : 15
   B) 16 : 9
   C) 17 : 9
   D) 9 : 17
   E) 15 : 7
   
   Answer & Explanation

   C) 17 : 9
   Explanation:
   Let radius = 5x and height = 12x
   Then slant height = √[(5x)² + (12x)²]= 13x
   Required ratio = 2ᴨr(h+r) : ᴨr(l+r)
   
   
9. A cone of radius 12 cm and height 5 cm is mounted on a cylinder of radius 12 cm and height 19 cm. Find the total surface area of the figure thus formed.
   A) 2498 cm²
   B) 2400 cm²
   C) 2476 cm²
   D) 2376 cm²
   E) 2546 cm²
   
   Answer & Explanation

   D) 2376 cm²
   Explanation:
   Slant height of cone, l = √(12² + 5²) = 13 cm
   Total surface area of final figure = curved surface area of cone + curved surface area of cylinder + area of base
   = ᴨrl + 2ᴨrh + ᴨr²
   = ᴨr (l + 2h + r)
   = (22/7) * 12 (13 + 2*19 +12)
   
   
10. How many spherical balls whose radius is half that of cylinder can be formed by melting a cylindrical iron rod whose height is eight times its radius?
    A) 44
    B) 48
    C) 60
    D) 56
    E) Cannot be determined
    
    Answer & Explanation

    B) 48
    Explanation:
    Let radius of rod = r, then height = 8r
    Radius of 1 spherical ball = r/2
    So number of balls = Vol. of cylindrical rod/Vol. of 1 spherical ball
    = ᴨ × r² × 8r / (4/3) × ᴨ × (r/2)³