Mathematics: 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.

3:21.5:14x6 inches, 8x12, 10x15 cm, 35 mm film, and most DSLR camerasStep-by-step explanation:hope that helps you out mate!!...

Two similar vases have heights which are in the ratio

hollymay808p0t9to

17.01.2022

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

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