Question

A cylinder of length 13cm has a volume 280 cm^3
Calculate the radius of the cylinder

b)The cylinder is placed in a box that is a cube of side 14 cm
Calculate the percentage of the volume of the box that is occupied by the cylinder

Answer 1

For first question :

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Radius\:of\:cylinder\approx2.61\:cm}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Height \: of \: cylinder = 13 \: cm \\ \\ \tt{:\implies Volume\:of\:cube=280\:cm^{3}} \\\\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Radius\:of\:cylinder=?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Volume \: of \: cylinder = \pi {r}^{2} h \\ \\ \tt: \implies 280 = 3.14 \times {r}^{2} \times 13 \\ \\ \tt: \implies \frac{280}{13 \times 3.14} = {r}^{2} \\ \\ \tt: \implies {r}^{2} = 6.85 \\ \\ \tt \implies r = \sqrt{6.85} \\ \\ \green{\tt: \implies r \approx 2.61 \: cm}$

For second question :

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Volume\:of\:cylinder=2156\:cm^{3}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Side \: of \: cube = 14 \: cm \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Volume\:of\:cylinder=?$

• According to given question :

$\circ \: \tt{Largest \: possible \: radius = 7 \: cm} \\ \\ \circ \: \tt{Largest \: possible \: height =14 \: cm}\\ \\ \bold{as \: we \: know \: that} \\ \tt: \implies Volume \: of \: cylinder = \pi {r}^{2} h \\ \\ \tt: \implies Volume \: of \: cylinder = \frac{22}{7} \times {7}^{2} \times 14 \\ \\ \tt: \implies Volume \: of \: cylinder =22 \times 7 \times 14 \\ \\ \green{\tt: \implies Volume \: of \: cylinder =2156 {cm}^{3} } \\ \\ \green{\tt{\therefore Largest \: possible \: cylinder \: can }} \\ \green{\tt{ \: \: \: \: cover \: in \: this \: cube \: is \: 2156 {cm}^{3} }}$

Answer 2

$\huge\bold\green{Question-1}$

A cylinder of length 13cm has a volume 280 cm³ .Calculate the radius of the cylinder ?

$\huge\bold\green{Answer}$

According to the question we have given :-

•°• Volume of Cube = 280 cm³

•°• Height of Cylinder = 13 cm

So, we have to find Radius of Cylinder

$\begin{lgathered}\ \sf =Volume_{cylinder} = \pi {r}^{2} h \\ \\ \sf = 280 = 3.14 \times {r}^{2} \times 13 \\ \\ \sf= \frac{280}{13 \times 3.14} = {r}^{2} \\ \\ \sf= {r}^{2} = 6.85 \\ \\ \sf = r = \sqrt{6.85} \\ \\ \sf = r = 2.61 \: cm^3 appx.\end{lgathered}$

Hence the required volume of cylinder is 2.61 cm³ (approximately)

$\huge\bold\green{Question-2}$

The cylinder is placed in a box that is a cube of side 14 cm . Calculate the percentage of the volume of the box that is occupied by the cylinder ?

$\huge\bold\green{Answer}$

According to the question we have given :-

•°• One Side of the Cube = 14 cm

So, we have to find Volume Of Cylinder

$\begin{lgathered}\sf={Largest \: Radius = 7 cm} \\ \: \tt={Largest \: Height = 14 cm}\\ \\ \\ \sf = Volume_{cylinder} = \pi {r}^{2} h \\ \\ \sf= Volume_{cylinder} = \frac{22}{7} \times {7}^{2} \times 14 \\ \\ \sf= Volume_{cylinder} =22 \times 7 \times 14 \\ \\ \sf = Volume_{cylinder} =2156 {cm}^{3}} \end{lgathered}$

Hence the larget cylinder is possible which can covers this cube have volume of 2156 cm³