Mathematics, 23.09.2019 15:30 asmaamasto

The volumes of two similar solids are 210 m3 and 1,680 m3. the surface area of the larger solid is 856 m2.
what is the surface area of the smaller solid?

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$\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{cccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\\\\\
-----------------------------\\\\

\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{s}{s}\implies \cfrac{\sqrt[3]{210}}{\sqrt[3]{1680}}=\cfrac{\sqrt{A}}{\sqrt{856}}$

solve for A

Answer from: mathfan5049

The surface area of smaller solid is:

214 m²

Step-by-step explanation:

Let A,V be the surface area and the volume of larger solid.

and A',V' be the surface area and volume of other solid.

We know that the ratio of volume to the surface area of the solid is given by:

$\dfrac{\sqrt{A}}{\sqrt{A'}}=\dfrac{\sqrt[3]{V}}{\sqrt[3]{V'}}$

On taking power 6 on both side we obtain:

$\dfrac{A^3}{A'^3}=\dfrac{V^2}{V'^2}$

We have:

V=210 m³ , V'=1680 m³

A=856 m²

Hence, we have:

$\dfrac{(856)^3}{A'^3}=\dfrac{(210)^2}{(1680)^2}\\\\\\A'^3=(107\times 2)^3\\\\\\A'=214\ m^2$

Hence, the surface area of solid is:

214 m²

Answer from: Quest

step-by-step explanation:

Which expression is equivalent to 24 1/3

Answer from: Quest

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation:

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The volumes of two similar solids are 210 m3 and 1,680 m3. the surface area of the larger solid is 8...

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