Question

A box in the shape of a cube has a surface area of 2400 cm?
What would be the volume of a similar box enlarged by a
scale factor of 1.5?​

Answer 1

$\sf{\huge{\underline{\red{Given :-}}}}$

• A box in the shape of a cube has a surface area of 2400 cm.

$\sf{\huge{\underline{To\:Find :-}}}$

• The volume of a similar box enlarged by a scale factor of 1.5.

$\sf{\huge{\underline{\green{Answer :-}}}}$

The surface area of the cube = 2400 cm.--(1)

We know, the surface area of the cube is 6a² --(2)

Comparing equation 1 & 2

6a² = 2400

➝ a² = 2400/6

➝ a² = 400

➝ a = √400

➝ a = 20

The similar box enlarged by a

scale factor of 1.5

20 × 1.5 = 30 cm

The volume of the box = a³

➝ 30 × 30 × 30

➝ 27000 cm³

Answer 2

Step-by-step explanation:

GIVEN:-

Area of a box = 2400cm^2

UNDERSTANDING THE CONCEPT:-

According to the question, The surface area of a cube is made up of 6 square faces. Because the surface area is 2400 cm², each face is 400 cm² and thus each edge of the cube is 20 cm.

(20 x 20 = 400)

Now we scale each edge up by 1.5 times,

20 x 1.5 = 30 cm.

REQUIRED ANSWER:-

So each edge in the similar box is 30 cm and the volume would be,

$v = 30 \times 30 \times 30$

$v = 27000cm {}^{3}$

SO, the volume of similar box = 27000cm^3