Answer:
The value of x is:
\(x=10\)
Step-by-step 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:
\(6.25\pi x=5\pi (x+2.5)\\\\i.e.\\\\6.25x=5(x+2.5)\\\\6.25x=5x+12.5\\\\6.25x-5x=12.5\\\\1.25x=12.5\\\\x=\dfrac{12.5}{1.25}\\\\x=10\)
