Two cubes each volume \( 125 \mathrm{~cm}^{3} \) are juined end to end Find the volaime and the surtace area of the resucting cubeid

The volume of each cube is given by \[ 125 \, \text{cm}^3. \] **Step 1. Find the side length of each cube:** Since the volume of a cube is \( s^3 \), we have \[ s^3 = 125 \quad \Rightarrow \quad s = \sqrt[3]{125} = 5 \, \text{cm}. \] **Step 2. Determine the dimensions of the resulting shape:** When two cubes are joined end to end, they form a cuboid with one dimension doubled. Thus, the dimensions of the cuboid are: - Length: \( 2s = 10 \, \text{cm} \) - Width: \( s = 5 \, \text{cm} \) - Height: \( s = 5 \, \text{cm} \) **Step 3. Calculate the volume of the resulting cuboid:** The volume is the sum of the volumes of the two cubes or can be computed using the dimensions of the cuboid. Using the cuboid dimensions: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = 10 \times 5 \times 5 = 250 \, \text{cm}^3. \] **Step 4. Calculate the surface area of the resulting cuboid:** The surface area of a cuboid with dimensions \( l \), \( w \), and \( h \) is given by \[ \text{Surface Area} = 2(lw + lh + wh). \] Substitute \( l = 10 \, \text{cm} \), \( w = 5 \, \text{cm} \), and \( h = 5 \, \text{cm} \): \[ \text{Surface Area} = 2\left(10 \times 5 + 10 \times 5 + 5 \times 5\right) = 2\left(50 + 50 + 25\right) = 2 \times 125 = 250 \, \text{cm}^2. \] **Answer:** - The volume of the resulting cuboid is \(\displaystyle 250 \, \text{cm}^3\). - The surface area of the resulting cuboid is \(\displaystyle 250 \, \text{cm}^2\).