Question

figure surface area

1. cylinder: height 40 m, base diameter 26 m, find its surface area
2. cylinder: height 4 mm, base radius 10 mm, find its surface area
3. cylinder: height 26 yd, base radius 11 yd, find its surface area

Explanation:

The total surface area of a cylinder is given by the formula:
$$SA = 2\pi r^2 + 2\pi rh = 2\pi r(r + h)$$
where $r$ is the radius and $h$ is the height of the cylinder.

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Cylinder 1 (26 m diameter, 40 m height)

Step1: Calculate the radius

Diameter $d=26\ \text{m}$, so $r=\frac{d}{2}=\frac{26}{2}=13\ \text{m}$

Step2: Plug values into formula

$$\begin{align*} SA&=2\pi(13)^2 + 2\pi(13)(40)\\ &=2\pi(169) + 2\pi(520)\\ &=338\pi + 1040\pi\\ &=1378\pi\\ &\approx1378\times3.14\\ &=4354.28\ \text{m}^2 \end{align*}$$

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Cylinder 2 (10 mm radius, 4 mm height)

Step1: Use given radius $r=10\ \text{mm}$, $h=4\ \text{mm}$

Step2: Plug values into formula

$$\begin{align*} SA&=2\pi(10)^2 + 2\pi(10)(4)\\ &=2\pi(100) + 2\pi(40)\\ &=200\pi + 80\pi\\ &=280\pi\\ &\approx280\times3.14\\ &=879.2\ \text{mm}^2 \end{align*}$$

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Cylinder 3 (11 yd radius, 26 yd height)

Step1: Use given radius $r=11\ \text{yd}$, $h=26\ \text{yd}$

Step2: Plug values into formula

$$\begin{align*} SA&=2\pi(11)^2 + 2\pi(11)(26)\\ &=2\pi(121) + 2\pi(286)\\ &=242\pi + 572\pi\\ &=814\pi\\ &\approx814\times3.14\\ &=2584.92\ \text{yd}^2 \end{align*}$$

Answer:

1. $\boldsymbol{4354.28\ \text{m}^2}$
2. $\boldsymbol{879.2\ \text{mm}^2}$
3. $\boldsymbol{2584.92\ \text{yd}^2}$