These cylinders are similar. Find the volume of

Mathematics

1 answer:

Basile [38]2 years ago

3 0

Answer:

$V_s=85\ cm^3$

Step-by-step explanation:

Let $V_s\ and\ V_b$ be the volumes of the smaller and bigger cylinder.

The formula for the volume of a cylinder is given by :

$V=\pi r^2 h$

As the two triangles are similar, the cube of their ratio would equal the ratio of their volume i.e.

$\dfrac{V_s}{V_b}=(\dfrac{h_s}{h_b})^3\\\\\dfrac{V_s}{V_b}=(\dfrac{3}{5})^3\\\\\dfrac{V_s}{V_b}=0.216\\\\V_s=393\times 0.216\\\\V_s=84.8\\\\or\\\\V=85\ cm^3$

So, the volume of the smaller cylinder is equal to $85\ cm^3$ .

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A quiz consists of 10 true or false questions. To pass the quiz a student must answer at least eight questions correctly.

lys-0071 [83]

Answer:

The probability of the student will pass the quiz = .0546

Step-by-step explanation:

Given -

Total no of question = 10

If the student guesses on each question there are two outcomes true of false

the probability of guesses question correctly = $\frac{1}{2}$

the probability of success is (p) = $\frac{1}{2}$

the probability of guesses question incorrectly = $\frac{1}{2}$

the probability of failure is (q) = 1- p = $\frac{1}{2}$

If the student guesses on each question he must answered at least 8 question correctly

the probability of the student will pass the quiz = $P(X\geq8 )$

= P(X = 8 ) + P(X = 9) + P(X = 10 )

= $\binom{10}{8}(p)^{8}(q)^{10 - 8} + \binom{10}{9}(p)^{9}(q)^{10 - 9} + \binom{10}{10}(p)^{10}(q)^{10 - 10}$

= $\frac{10!}{(2!)(8!)}(\frac{1}{2})^{8}(\frac{1}{2})^{10 - 8} +\frac{10!}{(1!)(9!)} (\frac{1}{2})^{9}(\frac{1}{2})^{10 - 9} + \frac{10!}{(0!)(10!)}(\frac{1}{2})^{10}(\frac{1}{2})^{10 - 10}$