Volume and Surface Area Questions Answers

Volume and Surface Area Questions Answers (MCQ) listings with explanations includes questions on Cubiod, Cube, Cylinder, Cone, Sphere, Hemisphere etc which are important for competitive exams like SSC, BANK PO, Clerk, IBPS, SBI-PO, RBI, MBA, MAT, CAT, IIFT, IGNOU, SSC CGL, CBI, CPO, CLAT, CTET, NDA, CDS, Specialist Officers.

11) The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km square. The height of mountain i

  • 1) 2.3 km
  • 2) 2.4 km
  • 3) 2.5 km
  • 4) 2.6 km
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Ans.   B
Explanation :
Let the radius of the base be r km. Then, \begin{aligned} \pi r^2 = 1.54 \r^2 = \frac{1.54*7}{22} = 0.49\= 0.7 km \\text{Now l=2.5 km, r = 0.7 km} \h = \sqrt{2.5^2 - 0.7^2} km \=\sqrt{6.25 - 0.49}\=\sqrt{5.76} km \= 2.4 km \end{aligned}

12) The radii of two cones are in ratio 2:1, their volumes are equal. Find the ratio of their heigh

  • 1) 1:4
  • 2) 1:3
  • 3) 1:2
  • 4) 1:5
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Ans.   A
Explanation :
Let their radii be 2x, x and their heights be h and H resp. Then, \begin{aligned} \text{Volume of cone =}\frac{1}{3}\pi r^2h \\frac{\frac{1}{3}*\pi *{(2x)}^2*h}{\frac{1}{3}*\pi *{x}^2*H} \=> \frac{h}{H} = \frac{1}{4} \=> h:H = 1:4 \end{aligned}

13) The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm

  • 1) \begin{aligned} 79.8 cm^3 \end{aligned}
  • 2) \begin{aligned} 79.4 cm^3 \end{aligned}
  • 3) \begin{aligned} 89.8 cm^3 \end{aligned}
  • 4) \begin{aligned} 89.4 cm^3 \end{aligned}
View Answer View Explanation
Ans.   C
Explanation :
Volume of the largest cone = Volume of the cone with diameter of base 7 and height 7 cm \begin{aligned} \text{Volume of cone =}\frac{1}{3}\pi r^2h \= \frac{1}{3}*\frac{22}{7}*3.5*3.5*7 \= \frac{269.5}{3}cm^3 \= 89.8 cm^3 \end{aligned} Note: radius is taken as 3.5, as diameter is 7 cm

14) The maximum length of a pencil that can he kept is a rectangular box of dimensions 8 cm x 6 cm x 2 cm,

  • 1) \begin{aligned} 2\sqrt{17} \end{aligned}
  • 2) \begin{aligned} 2\sqrt{16} \end{aligned}
  • 3) \begin{aligned} 2\sqrt{26} \end{aligned}
  • 4) \begin{aligned} 2\sqrt{24} \end{aligned}
View Answer View Explanation
Ans.   C
Explanation :
In this question we need to calculate the diagonal of cuboid, which is = \begin{aligned} \sqrt{l^2+b^2+h^2} \= \sqrt{8^2+6^2+2^2} \= \sqrt{104} \= 2\sqrt{26} \end{aligned}

15) Find the surface area of a 10cm*4cm*3cm bric

  • 1) 154 cm square
  • 2) 156 cm square
  • 3) 160 cm square
  • 4) 164 cm square
View Answer View Explanation
Ans.   D
Explanation :
Surface area of a cuboid = 2(lb+bh+hl) cm square So, Surface area of a brick = 2(10*4+4*3+3*10) cm square = 2(82) cm square = 164 cm square

16) A cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm. Find the total area of the wet surfac

  • 1) 42 m sqaure
  • 2) 49 m sqaure
  • 3) 52 m sqaure
  • 4) 64 m sqaure
View Answer View Explanation
Ans.   B
Explanation :
Area of the wet surface = 2[lb+bh+hl] - lb = 2 [bh+hl] + lb = 2[(4*1.25+6*1.25)]+6*4 = 49 m square

17) A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets into it. The mass of the man is

  • 1) 50 kg
  • 2) 60 kg
  • 3) 70 kg
  • 4) 80 kg
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Ans.   B
Explanation :
In this type of question, first we will calculate the volume of water displaces then will multiply with the density of water. Volume of water displaced = 3*2*0.01 = 0.06 m cube Mass of Man = Volume of water displaced * Density of water = 0.06 * 1000 = 60 kg

18) How many bricks, each measuring 25cm*11.25cm*6cm, will be needed to build a wall 8m*6m*22.

  • 1) 6100
  • 2) 6200
  • 3) 6300
  • 4) 6400
View Answer View Explanation
Ans.   D
Explanation :
To solve this type of question, simply divide the volume of wall with the volume of brick to get the numbers of required bricks So lets solve this Number of bricks = \begin{aligned} \frac{\text{Volume of wall}}{\text{Volume of 1 brick}} \= \frac{800*600*22.5}{25*11.25*6} \= 6400 \end{aligned}

19) A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume i

  • 1) 260
  • 2) 262
  • 3) 270
  • 4) 272
View Answer View Explanation
Ans.   C
Explanation :
Volume will be length * breadth * height, but in this case two heights are given so we will take average, \begin{aligned} Volume = \left(12*9*\left(\frac{1+4}{2}\right)\right)m^3 \12*9*2.5 m^3 = 270 m^3 \end{aligned}

20) The perimeter of one face of a cube is 20 cm. Its volume will b

  • 1) \begin{aligned} 125 cm^3 \end{aligned}
  • 2) \begin{aligned} 400 cm^3 \end{aligned}
  • 3) \begin{aligned} 250 cm^3 \end{aligned}
  • 4) \begin{aligned} 625 cm^3 \end{aligned}
View Answer View Explanation
Ans.   A
Explanation :
Edge of cude = 20/4 = 5 cm Volume = a*a*a = 5*5*5 = 125 cm cube
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