Question

4.6 surface area of prisms and cylinders
you are a technician working for a company that manufactures specialty fiberglass tanks. a customer has specified a cylindrical tank that has inside measurements of 10 meters tall and 5 meters in diameter. you will coat the inside of the wall and floor of the tank with an epoxy sealant. to calculate the amount of sealant to order, you need to find the surface area of the inner surfaces of the tank. what is the total area of the inner wall and the floor of the tank rounded to the nearest meter? use 3.14 for π.
the surface area of the inner wall and bottom of the tank is m²

Explanation:

Step1: Find the radius of the cylinder

The diameter $d = 5$ meters, so the radius $r=\frac{d}{2}=\frac{5}{2}= 2.5$ meters.

Step2: Calculate the area of the bottom - circle

The area of a circle is $A_{bottom}=\pi r^{2}$. Substituting $r = 2.5$ meters and $\pi=3.14$, we get $A_{bottom}=3.14\times(2.5)^{2}=3.14\times6.25 = 19.625$ square meters.

Step3: Calculate the lateral - surface area of the cylinder

The formula for the lateral - surface area of a cylinder is $A_{lateral}=2\pi rh$. Substituting $r = 2.5$ meters, $h = 10$ meters and $\pi = 3.14$, we have $A_{lateral}=2\times3.14\times2.5\times10=157$ square meters.

Step4: Calculate the total surface area of the inner wall and floor

$A = A_{lateral}+A_{bottom}=157 + 19.625=176.625\approx177$ square meters.

Answer:

177