Question

A kitchen sink has a volume of 1800 cubic inches.What is the volume of a similar sink that is larger by a scale factor of 2

Answer 1

Answer:

14400 cubic inches.

Step-by-step explanation:

Let l, b and h are length, breadth and height of a cuboid respectively, then

$V=l\times b\times h$

If another cuboid is larger by a scale factor of k, then kl, kb and kh are length, breadth and height of new cuboid respectively.

$V_1=kl\times kb\times kh$

$V_1=k^3(l\times b\times h)$

$V_1=k^3V$       ...(i)

It is given that a kitchen sink has a volume of 1800 cubic inches and a similar sink is larger by a scale factor of 2.

Substitute k=2 and V=1800 in equation (i).

$V_1=2^3(1800)$

$V_1=14400$

Therefore, the volume of required sink is 14400 cubic inches.