Question

A metal cube of edge 15cm is melted and recast into a square pyramid of base edge 25cm.what is its height?​

Answer 1

$\star \; {\underline{\boxed{\pmb{\blue{\frak{ \; Given \; :- }}}}}}$

• Edge of cube = 15 cm
• Edge of base of Square Pyramid = 25 cm

$\star \; {\underline{\boxed{\pmb{\orange{\frak{ \; To \; Find \; :- }}}}}}$

• Height of Pyramid = ?

$\star \; {\underline{\boxed{\pmb{\red{\frak{ \; Solution \; :- }}}}}}$

$\bigstar$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Volume{\small_{(Cube)}} = {Edge}^{3} }}}}}$

• ${\underline{\boxed{\pmb{\sf{ Volume{\small_{(Square \; Pyramid)}} = \dfrac{1}{3} \times {Edge}^{2} \times Height }}}}}$

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$\bigstar$ Calculating the Volume of Cube :

${\implies{\qquad{\sf{ Volume = {Edge}^{3} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Volume = {15}^{3} }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ Volume = 15 \times 15 \times 15 }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\purple{\sf{ Volume = 3375 \; {cm}^{3} }}}}}}}}$

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$\bigstar$ Calculating the Height of Pyramid :

${\dashrightarrow{\qquad{\sf{ Volume = \dfrac{1}{3} \times {Edge}^{2} \times Height }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 3375 = \dfrac{1}{3} \times {25}^{2} \times Height }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 3375 \times 3 = 1 \times {25}^{2} \times Height }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 10125 = {25}^{2} \times Height }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 10125 = 625 \times Height }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{10125}{625} = Height }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{10125}{625} = Height }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\pink{\sf{ Height = 16.2 \; cm }}}}}}}}$

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$\bigstar$ Therefore :

❛❛ Height of the Pyramid formed is 16.2 cm . ❜❜

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