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). [tex]\frac{V_{1}}{V_{2} }=(\frac{Side 1}{Side2})^{3}[/tex]
[tex]\frac{V_{1}}{V_{2} }=(\frac{3}{2})^{3}[/tex]
[tex]\frac{1080}{V_{2} }=(\frac{3}{2})^{3}[/tex]
[tex]\frac{1080}{V_{2} }=(\frac{27}{8})[/tex]
[tex]27V_{2}=8\times 1080[/tex]
[tex]V_{2}=\frac{8640}{27}[/tex]
[tex]V_{2}=320[/tex] cm³
b). Similarly ratio of the surface area of two vase will be
[tex]\frac{A_{1}}{A_{2} }=(\frac{Side 1}{Side2})^{2}[/tex]
[tex]\frac{A_{1}}{252}=(\frac{3}{2})^{2}[/tex]
[tex]\frac{A_{1}}{252}=(\frac{9}{4})[/tex]
[tex]A_{1}=\frac{9\times 252}{4}[/tex]
[tex]A_{1}=567[/tex] cm²
