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Question Detail
There are bricks with 24 cm x 12 cm x 8 cm dimensions. Find the total number of bricks required to construct a wall 24 m long, 8 m high and 60 m thick with 10% of wall filled with mortar.
- 35000
- 40000
- 45000
- 50000
Answer: Option C
Explanation:
So as per question,
\begin{aligned}
\text{Volume of wall} = (2400 * 800 * 60 ) cm^3 \\
\text{Volume of bricks} = \text { 90% of volume of wall } \\
= [ \frac{90}{100} * 2400 * 800 * 60 ] cm^3 \\
\text{ Volume of 1 brick = } (24 * 12 * 8) cm^3 \\
\text{Number of Bricks required} \\
= \frac{ (\frac{90}{100}) * (2400 * 800 * 60)}{24 * 12 * 8} \\
= 45000
\end{aligned}
1. 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}
2. The curved surface of a right circular cone of height 15 cm and base diameter 16 cm is:
- \begin{aligned} 116 \pi cm^2 \end{aligned}
- \begin{aligned} 122 \pi cm^2 \end{aligned}
- \begin{aligned} 124 \pi cm^2 \end{aligned}
- \begin{aligned} 136 \pi cm^2 \end{aligned}
Answer: Option 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}
3. 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) is:
- 4120 m cube
- 4140 m cube
- 5140 m cube
- 5120 m cube
Answer: Option 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.
4. 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 is :
- 2.3 km
- 2.4 km
- 2.5 km
- 2.6 km
Answer: Option 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}
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}
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