Question

The volume of a circular iron rod of length 1 m is 3850 cm. Find its diameter.
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Answer 1

Given:

• Volume of a circular iron rod is 3850 m³.
• Length of the rod is 1 m.

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To find:

• Diameter of the rod.

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Solution:

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As we know that, rod is in the shape of a right circular cylinder. We have volume and length (height) of the rod.

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We know that, volume of a cylinder is

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$\: \: \: \: \: \: \: \: \star\bf\: \: \: {Volume = \pi r^2 h}$

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$\tt\longrightarrow{Volume = 3850}$

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$\tt\longrightarrow{\dfrac{22}{7} \times r^2 \times 1 = 3850}$

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$\tt\longrightarrow{r^2 = \dfrac{3850 \times 7}{22}}$

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$\tt\longrightarrow{r^2 = 1225}$

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$\tt\longrightarrow{r = \sqrt{1225}}$

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$\tt\longrightarrow{r = 35}$

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Since, diameter is the double of radius, i.e., 2r

• Diameter = 2 × 35
• Diameter = 70m

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Hence,

• Diameter of the rod is 70m.

Answer 2

Step-by-step explanation:

${\large{\bold{\rm{\underline{Understanding\ the\ concept\ 1^{st}}}}}}$

★ This question says that the volume of a circular iron rod of length 1m is 3850m³. Through the given data we know that the rod is in the shape of a right circular cylinder. Here we use the concept of volume of cylinder. As the radius of the cylinder is not given. So first we will find the radius of the cylinder then we easily find out the diameter of the cylinder. So let's do....!!!

${\large{\bold{\rm{\underline{Given\ that}}}}}$

$\sf {\bigstar Volume\ of\ circular\ iron\ rod\ =\ 3850m^3.}$

$\sf {\bigstar Length\ of\ the\ rod\ =\ 1m.}$

${\large{\bold{\rm{\underline{To\ find}}}}}$

★ In this question we have to find the diameter of the rod ?

${\large{\bold{\rm{\underline{Using\ formula}}}}}$

$\star\;\underline{\boxed{\bf{\orange{Volume\ of\ cylinder\ =\ {\pi} r^2h.}}}}$

~Where,

• π, is greek letter for p.
• r, is for radius.
• h, is for height.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ Diameter of the rod is 70m.

${\large{\bold{\rm{\underline{Full\ solution}}}}}$

$\sf : \implies {Volume\ of\ cylinder\ =\ {\pi} r^2h}$

$\sf : \implies {\dfrac{22}{7} \times r^2\ \times 1\ =\ 3850}$

$\sf : \implies {r^2\ =\ \dfrac{3850 \times 7}{22}}$

$\sf : \implies {r^2\ =\ 1225}$

$\sf : \implies {r\ =\ \sqrt{1225}}$

$\sf : \implies {r\ =\ \bf 35.}$

~Since, we have to find out the diameter of the rod. Now we have the radius of the rod that is 35m. As we know that the diameter is the double of radius. So now we will find the diameter by multiplying 2 by the given radius.

$\sf : \implies {Diameter\ of\ rod\ =\ 2r}$

$\sf : \implies {Diameter\ of\ rod\ =\ 2 \times 35}$

$\sf : \implies {Diameter\ of\ rod\ =\ \bf 70m.}$

∴ Hence, the diameter of the rod is 70m.

${\large{\bold{\bf{\underline{\underline{More\ to\ know}}}}}}$

● Diagram of cylinder:

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{r}}\put(9,17.5){\sf{h}}\end{picture}$

$\bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto {C.S.A\ of\ cylinder\ =\ \bf 2{\pi}rh.}$

$\bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto {T.S.A\ of\ cylinder\ =\ \bf 2{\pi}r(r\ +\ h).}$

$\bf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto {Volume\ of\ cylinder\ =\ \bf {\pi}r^2h.}$