Question

A solid cuboid (28cm x 16cm x 11cm) made of iron is melted and re-casted to form a solid cylinder. Find the height of the cylinder if its radius is 28cm. do it fast I will gI've more points​

Answer 1

Given :

• Dimension of Cuboid = 28cm x 16cm x 11cm
• Radius of Cylinder = 28 cm

To Find :

• Height of Cylinder = ?

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SolutioN :

$\dag$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Volume {\small_{(Cylinder)}} = Length \times Width \times Height }}}}}$

• ${\underline{\boxed{\pmb{\sf{ Volume {\small_{(Cylinder)}} = \pi {r}^{2} h }}}}}$

$\maltese$ Calculating the Height :

$\begin{gathered} \; \; \longrightarrow \; \; \sf { Volume {\small_{(Cuboid)}} = Volume {\small_{(Cylinder)}} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { l \times w \times h = \pi {r}^{2} h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { 28 \times 16 \times 11 = \dfrac{22}{7} \times {28}^{2} \times h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { 28 \times 16 \times 11 = \dfrac{22}{7} \times 28 \times 28 \times h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { 448 \times 11 = \dfrac{22}{7} \times 28 \times 28 \times h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { 4928 = \dfrac{22}{\cancel7} \times \cancel{28} \times 28 \times h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { 4928 = 22 \times 4 \times 28 \times h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { 4928 = 88 \times 28 \times h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { 4928 = 88 \times 28 \times h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { 4928 = 2464 \times h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { \dfrac{4928}{2464} = h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; \sf { \cancel\dfrac{4928}{2464} = h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \longrightarrow \; \; {\underline{\boxed{\orange{\pmb{\sf { Height = 2 \; cm }}}}}} \; \bigstar \\ \\ \\ \end{gathered}$

$\therefore \;$ Height of the Cylinder is 2 cm .

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