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Question Detail
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 pipe.
- 3.696 kg
- 3.686 kg
- 2.696 kg
- 2.686 kg
Answer: Option 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
1. 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}
2. Two right circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of their radii.
- \begin{aligned} \sqrt{3}:1 \end{aligned}
- \begin{aligned} \sqrt{7}:1 \end{aligned}
- \begin{aligned} \sqrt{2}:1 \end{aligned}
- \begin{aligned} 2:1 \end{aligned}
Answer: Option 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}
3. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length if the wire in meters will be:
- 76 m
- 80 m
- 84 m
- 88 m
Answer: Option 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}
4. If a right circular cone of height 24 cm has a volume of 1232 cm cube, then the area of its curved surface is :
- \begin{aligned} 450 cm^2 \end{aligned}
- \begin{aligned} 550 cm^2 \end{aligned}
- \begin{aligned} 650 cm^2 \end{aligned}
- \begin{aligned} 750 cm^2 \end{aligned}
Answer: Option 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}
5. The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side.
- Rs. 850
- Rs. 860
- Rs. 876
- Rs. 886
Answer: Option C
Explanation:
We will first calculate the Surface area of cube, then we will calculate the quantity of paint required to get answer.
Here we go,
\begin{aligned}
\text{Surface area =}6a^2 \\
= 6 * 8^2 = 384 \text{sq feet} \\
\text{Quantity required =}\frac{384}{16} \\
= 24 kg\\
\text{Cost of painting =} 36.50*24 \\
= Rs. 876
\end{aligned}
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