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Question Detail
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 surface.
- 42 m sqaure
- 49 m sqaure
- 52 m sqaure
- 64 m sqaure
Answer: Option 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
1. 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 out.
- \begin{aligned} 40 m^3 \end{aligned}
- \begin{aligned} 42 m^3 \end{aligned}
- \begin{aligned} 44 m^3 \end{aligned}
- \begin{aligned} 46 m^3 \end{aligned}
Answer: Option C
Explanation:
\begin{aligned}
Volume = \pi r^2h \\
Volume = \left(\frac{22}{7}*1*1*14\right)m^3 \\
= 44 m^3
\end{aligned}
2. The radii of two cones are in ratio 2:1, their volumes are equal. Find the ratio of their heights.
- 1:4
- 1:3
- 1:2
- 1:5
Answer: Option 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}
3. 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 by:
- \begin{aligned} 11\frac{3}{7} cm \end{aligned}
- \begin{aligned} 11\frac{2}{7} cm \end{aligned}
- \begin{aligned} 11\frac{1}{7} cm\end{aligned}
- \begin{aligned} 11 cm\end{aligned}
Answer: Option 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}
4. A cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of the wood wasted is :
- 45%
- 56%
- 67%
- 75%
Answer: Option D
Explanation:
We will first subtract the cone volume from wood volume to get the wood wasted.
Then we can calculate its percentage.
\begin{aligned}
\text{Sphere Volume =}\frac{4}{3}\pi r^3 \\
\text{Cone Volume =}\frac{1}{3}\pi r^2h\\
\text{Volume of wood wasted =}\\
\left(\frac{4}{3}\pi *9*9*9\right)-\left(\frac{1}{3}\pi *9*9*9\right) \\
= \pi *9*9*9 cm^3 \\
\text{Required Percentage =} \\
\frac{\pi *9*9*9}{\frac{4}{3}\pi *9*9*9}*100 \% \\
= \frac{3}{4}*100 \% \\
= 75\%
\end{aligned}
5. 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. Find the diameter of each sphere.
- 4 cm
- 6 cm
- 8 cm
- 10 cm
Answer: Option A
Explanation:
In this type of question, just equate the two volumes to get the answer as,
\begin{aligned}
\text{Volume of cylinder =}\pi r^2h\\
\text{Volume of sphere =} \frac{4}{3}\pi r^3\\
=> 12*\frac{4}{3}\pi r^3 = \pi r^2h \\
=> 12*\frac{4}{3}\pi r^3 = \pi *8*8*2 \\
=> r^3 = \frac{8*8*2*3}{12*4} \\
=> r^3 = 8 \\
=> r = 2 cm \\
=> \text{Diameter =}2*2 = 4 cm
\end{aligned}
Thanks ! Your comment will be approved shortly !
-
Ajay 10 years ago
why we subtract lb from it
-
Admin 11 years ago
Dear Sachin,
As, we got,
2[lb+bh+hl] - lb
Open the bracket by multiplying by 2, we will get2lb + 2bh + 2hl - lb
= 2bh + 2 hl + lb
= 2 [bh + hl] + lbIn this way we got it.
-
Sachin 11 years ago
Can anyone please explain this formula step by step
2[lb+bh+hl] - lbHow did you got - lb
2 [bh+hl] + lb
How did you got + lb. Once the bracket are open, the sign should - not +
Will really appreciate for your reply
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