Question

Two similar vases have heights which are in the ratio 3 : 2.

(a) The volume of the larger vase is 1080 cm cube. Calculate the volume of the smaller vase.
(b) The surface area of the smaller vase is 252cm square. Calculate the surface area of the larger vase.

Answer 1

a). Volume of the smaller vase = 320 cm³

b). Surface area of the larger vase = 567 cm²

Explanation:

When we calculate the volume of any figure we multiply it's three dimensions either length, width, height or we do the cube of the radius (r×r×r=r³).

In other words volume is a three dimensional figure and surface area is two dimensional.

Therefore, ratio of volumes of two similar structures will be the ratio of cube of one side given.

a).
`(V_(1))/(V_(2) )=((Side 1)/(Side2))^(3)`

`(V_(1))/(V_(2) )=((3)/(2))^(3)`

`(1080)/(V_(2) )=((3)/(2))^(3)`

`(1080)/(V_(2) )=((27)/(8))`

`27V_(2)=8* 1080`

`V_(2)=(8640)/(27)`

`V_(2)=320` cm³

b). Similarly ratio of the surface area of two vase will be

`(A_(1))/(A_(2) )=((Side 1)/(Side2))^(2)`

`(A_(1))/(252)=((3)/(2))^(2)`

`(A_(1))/(252)=((9)/(4))`

`A_(1)=(9* 252)/(4)`

`A_(1)=567` cm²