Question

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

Answer 1

A)3 : 2
1080 : x
1 part = 360
2 *360 = 720

b) 3 :2 
x:252
1 part = 126
126*3 = 378
  :)

Answer 2

Answer:

a). Volume of the smaller vase = 320 cm³

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

Step-by-step 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). $\frac{V_{1}}{V_{2} }=(\frac{Side 1}{Side2})^{3}$

$\frac{V_{1}}{V_{2} }=(\frac{3}{2})^{3}$

$\frac{1080}{V_{2} }=(\frac{3}{2})^{3}$

$\frac{1080}{V_{2} }=(\frac{27}{8})$

$27V_{2}=8\times 1080$

$V_{2}=\frac{8640}{27}$

$V_{2}=320$ cm³

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

$\frac{A_{1}}{A_{2} }=(\frac{Side 1}{Side2})^{2}$

$\frac{A_{1}}{252}=(\frac{3}{2})^{2}$

$\frac{A_{1}}{252}=(\frac{9}{4})$

$A_{1}=\frac{9\times 252}{4}$

$A_{1}=567$ cm²