Mathematics, 13.01.2020 17:31 elijahjacksonrp6z2o7
Sphere a is similar to sphere b. the scale factor of the lengths of the radii of sphere a to sphere b is 1 to 4. sphere a has the radius of 6 units and a volume of 288pi cubic units. find the volume of sphere b.
Answers: 1
![\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}](/tpl/images/0453/0170/04ee6.png)
![\bf \cfrac{\textit{sphere A}}{\textit{sphere B}}\qquad \stackrel{\stackrel{sides'}{ratio}}{\cfrac{1}{4}}\qquad \qquad \stackrel{\stackrel{sides'}{ratio}}{\cfrac{1}{4}}=\stackrel{\stackrel{volumes'}{ratio}}{\cfrac{\sqrt[3]{288}}{\sqrt[3]{v}}}\implies \cfrac{1}{4}=\sqrt[3]{\cfrac{288}{v}}\implies \left( \cfrac{1}{4} \right)^3=\cfrac{288}{v} \\\\\\ \cfrac{1^3}{4^3}=\cfrac{288}{v}\implies \cfrac{1}{64}=\cfrac{288}{v}\implies v=18432](/tpl/images/0453/0170/7da71.png)
Other questions on the subject: Mathematics
Mathematics, 21.06.2019 22:10, carsondelane13
Monitors manufactured by tsi electronics have life spans that have a normal distribution with a standard deviation of 1800 hours and a mean life span of 20,000 hours. if a monitor is selected at random, find the probability that the life span of the monitor will be more than 17,659 hours. round your answer to four decimal places.
Answers: 2
You know the right answer?
Sphere a is similar to sphere b. the scale factor of the lengths of the radii of sphere a to sphere...
Questions in other subjects:
History, 31.03.2021 20:30
Mathematics, 31.03.2021 20:30
History, 31.03.2021 20:30
History, 31.03.2021 20:30
