Question

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)

Answer 1

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

Answer 2

The value of x is:

`x=10`

Explanation:

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

`\text{Volume}=\pi r^2h`

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

`\text{Surface\ area}=2\pi r(h+r)`

Now, based on the given question we have:

`r=2.5\ cm\ and\ h=x`

This means that:

`\text{Volume}=\pi (2.5)^2x\\\\i.e.\\\\Volume=6.25\pi x`

and

`\text{Surface\ area}=2\pi (2.5)(x+2.5)`

`\text{Surface\ area}=5\pi (x+2.5)`

Also, we have:

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

This means that:

`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=(12.5)/(1.25)\\\\x=10`