Question

A rectangular block of metal is 0.24 m long 0.19 m wide and 0.15 m high. lf the metal block is melted to form a cube, find the length of each side of the cube​

Answer 1

Answer:

Answer :

The required length of each side of the cube is approximately 0.1898 m

Step-by-step explanation :

Given :

A rectangular block of metal is 0.24 m long, 0.19 m wide and 0.15 m high.

The metal block is melted to form a cube.

To find :

The length of each side of the cube

Solution :

Let "l" be the length of the rectangular block

and b and h are width and height of the rectangular block respectively.

So,

l = 0.24 m

b = 0.19 m

h = 0.15 m

Since the rectangular block is melted to form a cube, the volume does not change.

So, Volume of rectangular block = Volume of the cube

Let's find the volume of rectangular block first.

Volume of the rectangular block = length × width × height

Substitute the values,

➙ Volume of the rectangular block = l × b × h

➙ Volume of the rectangular block = 0.24 m × 0.19 m × 0.15 m

➙ Volume of the rectangular block = 24 × 19 × 15 × 10⁻⁶ m³

➙ Volume of the rectangular block = 6840 × 10⁻⁶ m³

Let "a" m be the length of each side of the cube.

Volume of the cube = (side)³

➙ Volume of the cube = (a m)³

➙ Volume of the cube = a³ m³

Now, equal their volumes.

Volume of rectangular block = Volume of the cube

➛ 6840 × 10⁻⁶ m³ = a³ m³

➛ 6840 × 10⁻⁶ = a³

\begin{gathered}\rightarrow \sf a^3=6840 \times 10^{-6} \\\\ \rightarrow \sf a=\sqrt[3]{6840 \times 10^{-6}} \\\\ \rightarrow \sf a=\sqrt[3]{6840} \times 10^{-2} \\\\ \rightarrow \sf a \simeq 18.98 \times 10^{-2} \\\\ \rightarrow \sf a \simeq 0.1898 \ m\end{gathered}

→a

3

=6840×10

−6

→a=

3

6840×10

−6

→a=

3

6840

×10

−2

→a≃18.98×10

−2

→a≃0.1898 m

Therefore, the length of each side of the cube is approximately 0.1898 m