The lateral surface area of a cube is $256$ m $^{2}$ . The volume of the cube is:

512

^{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

64

^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

216

^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

256

^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $512$ m $^{3}$
Given, lateral surface area of a cube $= 256$ m $^{2}$ .

We know, lateral surface area of cube $= 4 ($ edge $)^{2}$ .
$∴ 4 ($ edge $)^{2} = 256$

$⟹ ($ edge $)^{2} = \frac{256}{4}$

$⟹ ($ edge $)^{2} = 64$

$⟹$ edge $= 8$ .

Also, volume of cube $= ($ edge $)^{3}$ .
$∴$ Volume of cube $= (8)^{3} = 512$ m $^{3}$ .

Therefore, option $A$ is correct.

Suggest Corrections

Similar questions

Question 7
The lateral surface area of a cube is $256 m^{2}$ . The volume of the cube is:

A) $512 m^{3}$
B) $64 m^{3}$
C) $216 m^{3}$
D) $256 m^{3}$

Q. The lateral surface area of a cube is 256 m². The volume of the cube is
(a) 64 m³
(b) 216 m³
(c) 256 m³
(d) 512 m³

Question 7
The lateral surface area of a cube is $256 m^{2}$ . The volume of the cube is:

A) $512 m^{3}$
B) $64 m^{3}$
C) $216 m^{3}$
D) $256 m^{3}$

Q. The lateral surface area of a cube is 256 m². The volume of the cube is ______.

The lateral surface area of a cube is 100 m². The volume of the cube is:

Join BYJU'S Learning Program

The lateral surface area of a cube is 256 m2. The volume of the cube is:

The correct option is A 512 m3Given, lateral surface area of a cube =256 m2.We know, lateral surface area of cube =4(edge)2.∴4(edge)2=256⟹(edge)2=2564⟹(edge)2=64⟹ edge =8.Also, volume of cube =( edge)3.∴ Volume of cube =(8)3=512 m3.Therefore, option A is correct.

The lateral surface area of a cube is $256$ m $^{2}$ . The volume of the cube is: