Unless stated otherwise, take . 2 cubes each of volume are joined end to end. Find the surface area of the resulting cuboid.

Question

Homi · Accepted Answer

We need to find the dimensions of the new shape first.

Step 1 — Find the side length of one cube

Let's find the side length of one cube. The volume of each cube is given. Volume of a cube is $a^3$ .

$a^3 = 64 \text{ cm}^3$

$a = \sqrt[3]{64}$

$\boxed{a = 4 \text{ cm}}$

Diagram 1

Step 2 — Find the dimensions of the resulting cuboid

Two cubes are joined end to end. This means one dimension will double. The other two dimensions will stay the same. Let the side length of each cube be 4 cm.

The new length of the cuboid will be $4 \text{ cm} + 4 \text{ cm}$ .

$l = 4 + 4$

$l = 8 \text{ cm}$

The breadth of the cuboid will be 4 cm.

$b = 4 \text{ cm}$

The height of the cuboid will be 4 cm.

$h = 4 \text{ cm}$

Diagram 2

Step 3 — Calculate the surface area of the cuboid

Now, let's calculate the surface area. The formula for the surface area of a cuboid is $2(lb + bh + hl)$ . We will use the dimensions we found. Length $l = \textbf{8 cm}$ , breadth $b = \textbf{4 cm}$ , height $h = \textbf{4 cm}$ .

$\text{Surface Area} = 2(lb + bh + hl)$

$= 2((8 \times 4) + (4 \times 4) + (4 \times 8))$

$= 2(32 + 16 + 32)$

$= 2(80)$

$\boxed{160 \text{ cm}^2}$

Answer

The surface area of the resulting cuboid is 160 cm².

Question 1

Answer

More questions in Exercise 12.1