Cylinders & Percentage Error
Learning Intent: Calculate Cylinder SA and justify measurement accuracy.
Cylinder Formula
A cylinder consists of two circles and one "rolled" rectangle.
$$TSA = 2\pi r^2 + 2\pi rh$$
Where $2\pi rh$ is the Curved Surface Area.
Percentage Error
Used to see how close an estimate is to the real value.
$$\% Error = \left| \frac{Approx - Exact}{Exact} \right| \times 100$$
QUIZ Test Yourself
Q1. Cylinder Surface Area
Calculate the TSA of a cylinder with radius $3\text{cm}$ and height $10\text{cm}$ (to 1 d.p.).
Show Answer
$2\pi(3)^2 + 2\pi(3)(10) \approx 56.5 + 188.5 = 245.0\text{cm}^2$
Q2. Error Calculation
You estimated a length as $50\text{m}$, but the exact length is $48\text{m}$. Find the % Error.
Show Answer
$| (50 - 48) / 48 | \times 100 = (2 / 48) \times 100 \approx 4.17\%$
Challenge Task
A soup can has a radius of $3.5\text{cm}$ and a height of $11\text{cm}$.
- Calculate the exact Total Surface Area using the $\pi$ button.
- Calculate the Area using $\pi \approx 3$.
- Determine the **Percentage Error** caused by using $\pi = 3$.