Question

A cube of side equal to 20 cm is open from the top. Its total surface area is __________ cm^2.

(a) 2000

(b) 2400

(c) 2500

(d) 8000

I have been asked this question by my college professor while I was bunking the class.

I need to ask this question from Surface Areas and Volumes topic in portion Surface Areas and Volumes of Mathematics – Class 9

Answer 1

To find the total surface area of a cube open from the top, we need to consider the surface area of all the sides except the top.

The formula for the total surface area $A$ of a cube with side length $a$ is:

Atotal=6a2A_{\text{total}} = 6a^2Atotal​=6a2

However, since the cube is open from the top, we exclude the area of the top face. So the total surface area of the open cube is:

Aopen=5a2A_{\text{open}} = 5a^2Aopen​=5a2

Given the side length of the cube $a=20\text{cm}$, we can calculate:

Aopen=5×(20)2=5×400=2000 cm2A_{\text{open}} = 5 \times (20)^2 = 5 \times 400 = 2000 \, \text{cm}^2Aopen​=5×(20)2=5×400=2000cm2

Therefore, the correct answer is:

(a) 2000