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}
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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}
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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
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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
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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
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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
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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}
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Ans. A
Explanation :
Edge of cude = 20/4 = 5 cm
Volume = a*a*a = 5*5*5 = 125 cm cube