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
