Question

A cylinder has volume of 154cm and a diameter of 7cm.find the height of the cylinder

Answer 1

Volume of cylinder given = 154 $cm^{3}$

diameter = 7 cm

so,

radius , r = $\frac{7}{2}$  cm

let height of cylinder be ' h '

then as we know,

volume of cylinder = π$r^{2} h$

154 = $\frac{22}{7} *(\frac{7}{2}) ^{2} *h$ =  $\frac{22}{7} *\frac{7}{2} *\frac{7}{2} *h$

154 = $22 * \frac{7}{4} * h$

h = $\frac{154*4}{22*7}$

h = 4 cm

SO THE HEIGHT OF THE CYLINDER WILL BE 4 CM.

Answer 2

$\large \bigstar\boxed{\bf \red{ GIVEN}} \bigstar \\ \\ \Longrightarrow \bf Diameter = 7 \: cm \\ \\\Longrightarrow \bf Radius = \frac{d}{2} = \frac{7}{2} cm \\ \\\Longrightarrow \bf Volume = 154 \: {cm}^{3}$

$\large \bigstar\boxed{\bf \red{TO \: FIND}} \bigstar \\ \\\Longrightarrow \bf Height \: of \: the \: cylinder$

$\large \bigstar\boxed{\bf \red{SOLUTION}} \bigstar \\ \\ \large \boxed{ \bf \orange{vol = \pi {r}^{2} h }}\\ \\ \Longrightarrow \bf 154 = \frac{ \cancel{22}}{ \cancel{7}} \times \frac{ \cancel7}{ \cancel{2}} \times \frac{7}{2} \times h \\ \\\Longrightarrow \bf 154 = \frac{77}{2} \times h \\ \\\Longrightarrow \bf h = 154 \times \frac{2}{77} \\ \\ \large\underline{\boxed{ \bf \green{ h = 4}}} \\ \\ \large\bf \blue {\mathtt{Height \: of \: cylinder \: is \: 4\: cm}}$