Question

The surface area of a cube whose volume is 343 is K \[c{m^2}\] the value of K is:
A) 180
B) 364
C) 294
D) 394

Answer 1

Hint: In this type of question we use formula of finding the volume of cube, with the help of volume we will find side and, after getting side we will find surface area by using the formula of surface area
Volume of cube with side a \[ = {a^3}\]
Surface area of cube with side a \[ = 6{a^2}\]

Complete step by step answer:
Volume of the cube is 343 \[c{m^3}\] is given.
As we are given volume if cube is 342 \[c{m^3}\],
Let say side of cube is a cm then
Volume of cube = 343
Substitute volume = 343
\[343 = {a^3}\]
\[a = {(343)^{\left( {\dfrac{1}{3}} \right)}}\]
\[a = 7\]
After solving the above equation, we get a = 7
It means side of a square is 7 cm
Now we have to find the surface area of the cube
As we mentioned surface area of cube with side a \[ = 6{a^2}\]
Substitute a = 7
Surface area of cube with side a is \[ = 6{(7)^2}\]
Surface area of cube with side a is \[ = 6 \times 49\]
Surface area of cube with side a is \[ = 294\]
It means Surface area of cube with side a is cm

Hence, we can clearly say that option (c) is correct .

Note: In this type of question we need to know the formula of finding the volume of the cube and finding the surface area by using the side of the cube. We should know how to calculate \[a = {(343)^{\left( {\dfrac{1}{3}} \right)}}\] it will make calculation faster.
Multiplication should be done carefully as there are chances of making mistakes.