The value of the solid's surface area is equal to the value of the solid's volume. Find the value of x. (Cylinder with a radius of 2.5 cm and height of x)

interesting

V=hpir^2
SA=2pir^2+2hpir

then r=2.5 and x=? and V=SA then

xpi2.5^2=2pi2.5^2+2xpi2.5
xpi2.5^2=(2.5pi)(2*2.5+2x)
divide both sides by 2.5pi
2.5x=5+2x
minus 2x from both sides
0.5x=5
divide oth sides by 0.5
x=10

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lidaralbany lidaralbany · Answer 2 · 2019-09-23T13:35:34+02:00

Answer:

The value of x is:

[tex]x=10[/tex]

Step-by-step explanation:

We know that for a cylinder with radius r and height h the volume of the solid is given by:

[tex]\text{Volume}=\pi r^2h[/tex]

Also, the surface area of a cylinder is given by:

[tex]\text{Surface\ area}=2\pi r(h+r)[/tex]

Now, based on the given question we have:

[tex]r=2.5\ cm\ and\ h=x[/tex]

This means that:

[tex]\text{Volume}=\pi (2.5)^2x\\\\i.e.\\\\Volume=6.25\pi x[/tex]

and

[tex]\text{Surface\ area}=2\pi (2.5)(x+2.5)[/tex]

[tex]\text{Surface\ area}=5\pi (x+2.5)[/tex]

Also, we have:

The value of the solid's surface area is equal to the value of the solid's volume.

This means that:

[tex]6.25\pi x=5\pi (x+2.5)\\\\i.e.\\\\6.25x=5(x+2.5)\\\\6.25x=5x+12.5\\\\6.25x-5x=12.5\\\\1.25x=12.5\\\\x=\dfrac{12.5}{1.25}\\\\x=10[/tex]