1) If the volume of two cubes are in the ratio 27:1, the ratio of their edges i
- 1) 3:1
- 2) 3:2
- 3) 3:5
- 4) 3:7
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Ans. A
Explanation :
Let the edges be a and b of two cubes, then
\begin{aligned}
\frac{a^3}{b^3} = \frac{27}{1} \=> \left( \frac{a}{b} \right)^3 = \left( \frac{3}{1} \right)^3 \\frac{a}{b}=\frac{3}{1} \=> a:b = 3:1
\end{aligned}
2) A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug o
- 1) \begin{aligned} 40 m^3 \end{aligned}
- 2) \begin{aligned} 42 m^3 \end{aligned}
- 3) \begin{aligned} 44 m^3 \end{aligned}
- 4) \begin{aligned} 46 m^3 \end{aligned}
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Ans. C
Explanation :
\begin{aligned}
Volume = \pi r^2h \Volume = \left(\frac{22}{7}*1*1*14\right)m^3 \= 44 m^3
\end{aligned}
3) Two right circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of their radi
- 1) \begin{aligned} \sqrt{3}:1 \end{aligned}
- 2) \begin{aligned} \sqrt{7}:1 \end{aligned}
- 3) \begin{aligned} \sqrt{2}:1 \end{aligned}
- 4) \begin{aligned} 2:1 \end{aligned}
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Ans. C
Explanation :
Let their heights be h and 2h and radii be r and R respectively then.
\begin{aligned}
\pi r^2h = \pi R^2(2h) \=> \frac{r^2}{R^2} = \frac{2h}{h} \= \frac{2}{1} \=> \frac{r}{R} = \frac{\sqrt{2}}{1} \=> r:R = \sqrt{2}:1 \\end{aligned}
4) A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop
- 1) \begin{aligned} 11\frac{3}{7} cm \end{aligned}
- 2) \begin{aligned} 11\frac{2}{7} cm \end{aligned}
- 3) \begin{aligned} 11\frac{1}{7} cm\end{aligned}
- 4) \begin{aligned} 11 cm\end{aligned}
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Ans. A
Explanation :
Let the drop in the water level be h cm, then,
\begin{aligned}
\text{Volume of cylinder= }\pi r^2h \=> \frac{22}{7}*\frac{35}{2}*\frac{35}{2}*h = 11000 \=> h = \frac{11000*7*4}{22*35*35}cm\= \frac{80}{7}cm\= 11\frac{3}{7} cm
\end{aligned}
5) 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length if the wire in meters will b
- 1) 76 m
- 2) 80 m
- 3) 84 m
- 4) 88 m
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Ans. C
Explanation :
Let the length of the wire be h
\begin{aligned}
Radius = \frac{1}{2}mm = \frac{1}{20}cm\\pi r^2h = 66 \\frac{22}{7}*\frac{1}{20}*\frac{1}{20}*h = 66 \=> h = \frac{66*20*20*7}{22} \= 8400 cm \= 84 m
\end{aligned}
6) A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weights 8g/cm cube, then find the weight of the pip
- 1) 3.696 kg
- 2) 3.686 kg
- 3) 2.696 kg
- 4) 2.686 kg
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Ans. A
Explanation :
In this type of question, we need to subtract external radius and internal radius to get the answer using the volume formula as the pipe is hollow. Oh! line become a bit complicated, sorry for that, lets solve it.
External radius = 4 cm
Internal radius = 3 cm [because thickness of pipe is 1 cm]
\begin{aligned}
\text{Volume of iron =}\pi r^2h\= \frac{22}{7}*[4^2 - 3^2]*21 cm^3\= \frac{22}{7}*1*21 cm^3\= 462 cm^3 \\end{aligned}
Weight of iron = 462*8 = 3696 gm
= 3.696 kg
7) How many cubes of 10 cm edge can be put in a cubical box of 1 m edg
- 1) 10000 cubes
- 2) 1000 cubes
- 3) 100 cubes
- 4) 50 cubes
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Ans. B
Explanation :
\begin{aligned}
\text{Number of cubes =}\frac{100*100*100}{10*10*10} \= 1000
\end{aligned}
Note: 1 m = 100 cm
8) The curved surface of a right circular cone of height 15 cm and base diameter 16 cm
- 1) \begin{aligned} 116 \pi cm^2 \end{aligned}
- 2) \begin{aligned} 122 \pi cm^2 \end{aligned}
- 3) \begin{aligned} 124 \pi cm^2 \end{aligned}
- 4) \begin{aligned} 136 \pi cm^2 \end{aligned}
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Ans. D
Explanation :
\begin{aligned}
\text{Curved surface area of cone=}\pi rl\l = \sqrt{r^2+h^2} \l = \sqrt{8^2+15^2} = 17cm \
\text{Curved surface area =}\pi rl\= \pi *8*17 = 136 \pi cm^2
\end{aligned}
9) If a right circular cone of height 24 cm has a volume of 1232 cm cube, then the area of its curved surface i
- 1) \begin{aligned} 450 cm^2 \end{aligned}
- 2) \begin{aligned} 550 cm^2 \end{aligned}
- 3) \begin{aligned} 650 cm^2 \end{aligned}
- 4) \begin{aligned} 750 cm^2 \end{aligned}
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Ans. B
Explanation :
Volume is given, we can calculate the radius from it, then by calculating slant height, we can get curved surface area.
\begin{aligned}
\frac{1}{3}*\pi *r^2*h = 1232 \\frac{1}{3}*\frac{22}{7}*r^2*24 = 1232 \r^2 = \frac{1232*7*3}{22*24} = 49 \r = 7 \\text{Now, r = 7cm and h = 24 cm } \l = \sqrt{r^2+h^2} \= \sqrt{7^2+24^2} = 25cm \\text{Curved surface area =}\pi rl\= \frac{22}{7}*7*25 = 550 cm^2
\end{aligned}
10) A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube)
- 1) 4120 m cube
- 2) 4140 m cube
- 3) 5140 m cube
- 4) 5120 m cube
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Ans. D
Explanation :
l = (48 - 16)m = 32 m, [because 8+8 = 16]
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m cube
= 5120 m cube.