Calculate Surface Area: Cuboid with 25 cm² Base and 3 cm Height

Given the cuboid whose square base is of size 25 cm²,

The height of the cuboid is 3 cm,

What is the surface area of the cuboid?

Video Solution

Solution Steps

00:00 Calculate the surface area of the box

00:03 It's a square according to the given data, so all sides are equal

00:07 We'll use the formula for calculating the area of a square (side squared)

00:10 We'll substitute appropriate values and solve for side A

00:13 This is side A

00:24 Now we'll use the formula for calculating the surface area of a box

00:33 We'll substitute appropriate values and solve for the surface area

01:21 And this is the solution to the question

Step-by-Step Solution

Let's find the surface area of the cuboid step by step:

First, we determine the side length of the square base. Since the area of the square base is given as $25 \, \text{cm}^2$ , we have:

s^2 = 25 \implies s = \sqrt{25} = 5 \, \text{cm}

Now, using the surface area formula for a cuboid with a square base:

\text{Surface Area} = 2s^2 + 4s \times h

Substitute the values $s = 5 \, \text{cm}$ and $h = 3 \, \text{cm}$ :

\text{Surface Area} = 2(5^2) + 4(5)(3) = 2(25) + 60 = 50 + 60 = 110 \, \text{cm}^2

Therefore, the surface area of the cuboid is 110 cm².