Question

the volume of a cylinder is 448π cm³ and height 7cm. find its diameter..​

Answer 1

$\huge{\mathtt{{\red{\boxed{\tt{\pink{\orange{Ans}\purple{wer}}}}}}}}$

$\sf{\underline{\overline{\red{Given\::-}}}}$

•Volume of a cylinder----

$448\pi {cm}^{3}$

•Height of the cylinder=7cm

$\sf{\underline{\overline{\pink{To\:Find\::-}}}}$

•Diameter of the cylinder

$\sf{\underline{\overline{\orange{Solution\::-}}}}$

We know that volume of a cylinder is -----

= > $\pi {r}^{2} h$

= > $\pi \times {r}^{2} \times 7 = 448\pi$

= > ${r}^{2} = \frac{448\pi}{7\pi}$

= >${r}^{2} = 64$

= > $r = \sqrt{64}$

= >$r \:= 8\:cm\:$

Thus,radius of the cylinder is 8cm

Hence,diameter=2(8)

=>16cm

Answer 2

Answer:

Diagram :

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{8\ cm}}\put(9,17.5){\sf{7\ cm}}\end{picture}$

$\begin{gathered}\end{gathered}$

Given :

• Volume of cylinder = 448π cm³.
• Height of cylinder = 7 cm.

$\begin{gathered}\end{gathered}$

To Find :

• Diameter of cylinder

$\begin{gathered}\end{gathered}$

Solution :

☼ Here, I am doing the solution by two methods.

$\star \: {\underline{\underline{\sf{ \red{First \: Method \::}}}}}$

☼ Finding the radius of cylinder by substituting the values in the formula :-

${\longrightarrow{\small{\underline{\boxed{\pmb{\sf{V = \pi {r}^{2} h}}}}}}}$

☼ Where :-

• V = Volume
• π = 22/7
• r = radius
• h = height

☼ Now :-

${\longrightarrow{\small{\sf{V = \pi {r}^{2} h}}}}$

${\longrightarrow{\small{\sf{448 \pi = \pi {r}^{2} 7}}}}$

${\longrightarrow{\small{\sf{448 \times \dfrac{22}{7} = \dfrac{22}{7} \times {r}^{2} \times 7}}}}$

${\longrightarrow{\small{\sf{\cancel{448} \times \dfrac{22}{\cancel{7}}= \dfrac{22}{\cancel{7}}\times {r}^{2} \times \cancel{7}}}}}$

${\longrightarrow{\small{\sf{64 \times 22= 22{r}^{2} }}}}$

${\longrightarrow{\small{\sf{1408= 22{r}^{2} }}}}$

${\longrightarrow{\small{\sf{{r}^{2} = \dfrac{1408}{22}}}}}$

${\longrightarrow{\small{\sf{{r}^{2} = \cancel\dfrac{1408}{22}}}}}$

${\longrightarrow{\small{\sf{{r}^{2} = 64}}}}$

${\longrightarrow{\small{\sf{r = \sqrt{64}}}}}$

${\longrightarrow{\small{\sf{r = \sqrt{8 \times 8}}}}}$

${\longrightarrow{\small{\underline{\underline{\sf{r = 8 \: cm}}}}}}$

${\longrightarrow{\small{\underline{\boxed{\sf{\pink{Radius = 8 \: cm}}}}}}}$

∴ The radius of cylinder is 8 cm.

$\rule{200}2$

☼ Now, finding the diameter of cylinder :-

${\longrightarrow{\small{\underline{\boxed{\pmb{\sf{d = 2r}}}}}}}$

☼ Where :-

• d = diameter
• r = radius

☼ Now :-

${\longrightarrow{\small{\sf{d = 2r}}}}$

${\longrightarrow{\small{\sf{d = 2 \times 8}}}}$

${\longrightarrow{\small{\underline{\underline{\sf{d = 16 \: cm}}}}}}$

${\longrightarrow{\small{\underline{\boxed{\sf{\pink{Diameter = 16 \: cm}}}}}}}$

∴ The diameter of cylinder is 16 cm.

$\begin{gathered}\end{gathered}$

$\star \: {\underline{\underline{\sf{\red{Second\: Method \::}}}}}$

☼ Finding the diameter of cylinder by substituting the values in formula :-

${\longrightarrow{\small{\underline{\boxed{\pmb{\sf{d= 2 \times \sqrt{\dfrac{v}{{\pi}h}}}}}}}}}$

Now :-

${\longrightarrow{\small{\sf{d= 2 \times \sqrt{\dfrac{v}{{\pi}h}}}}}}$

${\longrightarrow{\small{\sf{d= 2 \times \sqrt{\dfrac{448 \pi}{{\pi}h}}}}}}$

${\longrightarrow{\small{\sf{d= 2 \times \sqrt{\dfrac{448 \times \dfrac{22}{7} }{\dfrac{22}{7} \times 7}}}}}}$

${\longrightarrow{\small{\sf{d= 2 \times \sqrt{\dfrac{\cancel{448} \times \dfrac{22}{\cancel{7}}}{\dfrac{22}{\cancel{7}}\times \cancel{7}}}}}}}$

${\longrightarrow{\small{\sf{d= 2 \times \sqrt{\dfrac{64 \times 22}{22}}}}}}$

${\longrightarrow{\small{\sf{d= 2 \times \sqrt{\dfrac{1408}{22}}}}}}$

${\longrightarrow{\small{\sf{d= 2 \times \sqrt{\cancel{\dfrac{1408}{22}}}}}}}$

${\longrightarrow{\small{\sf{d= 2 \times \sqrt{64}}}}}$

${\longrightarrow{\small{\sf{d= 2 \times \sqrt{8 \times 8}}}}}$

${\longrightarrow{\small{\sf{d= 2 \times 8}}}}$

${\longrightarrow{\small{\underline{\underline{\sf{d = 16 \: cm}}}}}}$

${\longrightarrow{\small{\underline{\boxed{\sf{\pink{Diameter = 16 \: cm}}}}}}}$

∴ The diameter of cylinder is 16 cm.

$\begin{gathered}\end{gathered}$

Learn More :

$\begin{gathered}\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}\end{gathered}$

$\rule{200}2$