Question

The lateral surface area of the cube is 900 sq. cm.Find its volume.

Answer 1

Answer:

lateral surface area of cube = 4a^2 = 900

a^2 = 900/4

a = 150cm

Total surface area = 6a^2

= 6(150)^2

= 135000 cm sq.

volume of cube = side cube

=(150)^3

=3,376,000 cm cube.

Answer 2

${\underline{\underline{\bf{Given:}}}}$

• Lateral Surface Area of a cube = 900 cm².

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The Volume of the cube.

${\underline{\underline{\bf{Formulae\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{LSA}_{(Cube)}={4a}^{2}\:sq.units}}}$

$\underline{\boxed{\sf{{Volume}_{(Cube)}={a}^{3}\:cu.units}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\bullet{\sf{\:a=side}}$

${\underline{\underline{\bf{Solution:}}}}$

The volume of the cube has to be found. We know the LSA of the cube. To find the volume, the measure of side is required. Side can be found by substituting the given measure in the formula of LSA of cube. Then, substitute the measure of side obtained in the formula of volume of cube. The required answer will be obtained.

Side of the cube:

$\:\:\:\implies{\sf{{LSA}_{(Cube)}={4a}^{2}\:sq.units}}$

$\:\:\:\implies{\sf{900={4a}^{2}}}$

$\:\:\:\implies{\sf{\frac{900}{4}={a}^{2}}}$

$\:\:\:\implies{\sf{225=a^2}}$

$\:\:\:\implies{\sf{\sqrt{225}=a}}$

$\:\:\:\implies{\underline{\underline{\sf{15\:cm=a}}}}$

★ Volume of the cube:

$\:\:\:\implies{\sf{{Volume}_{(Cube)}={a}^{3}\:cu.units}}$

$\:\:\:\implies{\sf{{Volume}_{(Cube)}=15^3}}$

$\:\:\:\implies{\sf{\red{\underline{\underline{{Volume}_{(Cube)}=3375\:{cm}^{3}}}}}}$

${\underline{\underline{\bf{Required\:answer:}}}}$

• The volume of the cube whose LSA is 900 cm² is 3375 cm³.

__________________________________________