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2 years ago

The radius of a cylinder is increased by 5 percent. Given that the height is constant, find the percentage increase in volume.

Mathematics

1 answer:

telo118 [61]2 years ago

7 0

Step-by-step explanation:

Volume =pir^h

V1=pi r1^h

V2=pir2^2h

Now,V1/V2=r1^2/r2^2

v1/v2=r1^2/(1.05)^2 ((r2=r1+5/100r1)

v1/v2=1/1.1025

v1/v2=0.907

(v1/v2-1)=0.0907×100%

(v1-v2)/v2=9.07%

increase in volume is 9.07%

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KatRina [158]

Answer: Third Option

$x=1.469743$

Step-by-step explanation:

We have the following exponential equation

$3^{x+1}=15$

We must solve the equation for the variable x

To clear the variable x apply the $log_3$ function on both sides of the equation

$log_3(3^{x+1})=log_3(15)$

Simplifying we get the following:

$x+1=log_3(15)$

To simplify the expression $log_3 (15)$ we apply the base change property

$log_b(y)=\frac{log(y)}{log(b)}$

This means that:

$log_3 (15)=\frac{log(15)}{log(3)}$

Then:

$x+1=\frac{log(15)}{log(3)}$

$x=\frac{log(15)}{log(3)}-1$

$x=1.469743$

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The radius of a cylinder is increased by 5 percent. Given that the height is constant, find the percentage increase in volume. ​

The radius of a cylinder is increased by 5 percent. Given that the height is constant, find the percentage increase in volume.