Question

Cardboard costs $3.5 per. cm2 How much will a jewellery box of dimensions 15 cm×10 cm×5 cm cost if it is made using this cardboard?

Answer 1

Answer:

$1925

Solution:

⇒ Given:

Length of the box = 15 cm

Breadth of the box = 10 cm

Height of the box = 5 cm

Cost of 1 cm² cardboard = $3.5

In this question, we need to use the concept of Total Surface Area [TSA] of a cuboid. A jewellery box is a completely closed box, hence we need not exclude the area of any surface.

Formula:

$\sf{\boxed{TSA\:of\:a\:cuboid=2(lh+bh+lb)}}$

Substituting the values in the equation:

TSA = 2 [(15x5)+(10x5)+(15x10)]

= 2 x [75 + 50 + 150]

= 2 x 275

= 550 cm²

It is given that the cost of 1 cm² cardboard = $3.5

So, cost of 550 cm² cardboard = $3.5 x 550

= $1925

Hence the required cost is $1925.

Knowledge Bytes:

→ Formulae related to a cuboid:

✳ LSA = 2 (lh + bh)

✳ TSA = 2 (lh + bh + lb)

✳ Volume = lbh

✳ To find area of a box with one side open or to whitewash a room of 4 walls

= 2 (lh + bh) + lb

Answer 2

Solution:-

⇒ Given:

Length of the box = 15 cm

Breadth of the box = 10 cm

Height of the box = 5 cm

Cost of 1 cm² cardboard = $3.5

In this question, we need to use the concept of Total Surface Area [TSA] of a cuboid. A jewellery box is a completely closed box, hence we need not exclude the area of any surface.

Substituting the values in the equation:

TSA = 2 [(15x5)+(10x5)+(15x10)]

= 2 x [75 + 50 + 150]

= 2 x 275

= 550 cm²

It is given that the cost of 1 cm² cardboard = $3.5

So, cost of 550 cm² cardboard = $3.5 x 550

= $1925

Hence the required cost is $1925.