Math CentralQuandaries & Queries


Question from Jordan, a student:

This cylinder is given:

Cylinder with a height of 84 cm and a diameter of 54 cm.

Question: The exterior of the drum (cylinder), except the base, is to be painted blue. calculate how many litres of paint will be needed to paint 400 drums if one litre of paint covers 8.8meters Squared.
Answer to nearest tenth of a litre.

what i did was find the total surface area, then subtract the base which is pi(radius)squared from the total surface area.
then i multiplied that by 400 and then converted the 8.8 meters to cm and divided that from the Surface Area but still got the wrong answer according to the answer key

Answer Key Says the Answer is 78.4 L

What am i doing wrong? how do i solve this question? please explain step by step for me to follow easily.

Thank you so much for your time and effort!!!

Hi Jordan,

I approach was essentially the same as yours. The area of the side of a drum is $2 \times \pi \times r \times h$ where $r$ is the radius of the top and $h$ is the base. That gave me

\[2 \times \pi \times 27 \times 54 = 14250.26 \mbox{ cm}^2\]

The area of the bottom is

\[\pi \times r^2 = \pi \times 27^2 = 2290.22 \mbox{ cm}^2\]

Thus the total surface area is

\[14250.26 + 2290.22 = 16540.49 \mbox{ cm}^2\]

$8.8 m^2 = 8.8 \times 100 \times 100 = 88000 \mbox{ cm}^2$ and hence each drum requires

\[\frac{16540.49}{88000} = 0.18796 \mbox{ liters of paint.}\]

Thus you need $0.18796 \times 400 = 75.2$ liters.

Is that what you got?

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