Mathematics, 06.10.2019 12:30 cheyannehatton

"if the volume of two cylinders are equal, then their surfaces areas must be equal." do you agree or disagree with this statement? why or why not? what experiment would you devise to prove that you are correct?

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Answer from: davin74

Check the picture below, same volumes.

$\bf \textit{surface area of a cylinder}\\\\
S=2\pi r(h+r)\\\\
-------------------------------\\\\
\textit{for the short cylinder}\quad 
\begin{cases}
r=3\\
h=10
\end{cases}\implies S=2\pi 3(10+3)
\\\\\\
\boxed{S=78\pi }\\\\
-------------------------------\\\\
\textit{for the tall cylinder}\quad 
\begin{cases}
r=2\\
h=22.5
\end{cases}\implies S=2\pi 2(22.5+2)
\\\\\\
\boxed{S=98\pi }$

if the volume of two cylinders are equal, then their surfaces areas must be equal. do you agree or

if the volume of two cylinders are equal, then their surfaces areas must be equal. do you agree or

Answer from: leledaisy1994

This statement is true, because the surface area and the volume depend on the same variables.

$V_{1} =V_{1} \implies (r_{1} =r_{2} ) \ and \ (h_{1} =h_{2} )$

Step-by-step explanation:

The volume of a cylinder is defined as

$V=\pi \times r^{2} \times h$

The surface area of a cylinder is defined as

$S=2 \pi r^{2} + 2\pi rh$

Notice that if two cylinder have the same volume that means the radius and height are also equal.

$V_{1} =V_{1} \implies (r_{1} =r_{2} ) \ and \ (h_{1} =h_{2} )$

Now, if you analyse the surface definition of a cylinder, you would find that it depends on the radius and the height, which means if these variables are equal, then the area surfaces are also equal, like in this case.

Therefore, this statement is true, because the surface area and the volume depend on the same variables.

Answer from: Quest

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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