Math / Geometry

Questiona) Calculate the curved surface area. b) Calculate the total surface area.
Give each answer to 1 d.p. Watch video

Studdy Solution

STEP 1

1. The cylinder has a height of $6$ cm.
2. The radius of the base of the cylinder is $7$ cm.
3. The curved surface area (CSA) of a cylinder is calculated using the formula $2\pi rh$ .
4. The total surface area (TSA) of a cylinder includes the curved surface area and the areas of the two circular bases, calculated using the formula $2\pi rh + 2\pi r^2$ .

STEP 2

1. Calculate the curved surface area (CSA).
2. Calculate the total surface area (TSA).

STEP 3

Calculate the curved surface area (CSA) using the formula:
$\text{CSA} = 2\pi rh$
Substitute the given values:
$\text{CSA} = 2\pi \times 7 \text{ cm} \times 6 \text{ cm}$
Calculate:
$\text{CSA} = 2\pi \times 42 \text{ cm}^2$ $\text{CSA} = 84\pi \text{ cm}^2$
Use $\pi \approx 3.1416$ :
$\text{CSA} \approx 84 \times 3.1416 \text{ cm}^2$ $\text{CSA} \approx 263.9 \text{ cm}^2$

STEP 4

Calculate the total surface area (TSA) using the formula:
$\text{TSA} = 2\pi rh + 2\pi r^2$
Substitute the given values:
$\text{TSA} = 2\pi \times 7 \text{ cm} \times 6 \text{ cm} + 2\pi \times 7^2 \text{ cm}^2$
Calculate:
$\text{TSA} = 84\pi \text{ cm}^2 + 98\pi \text{ cm}^2$ $\text{TSA} = 182\pi \text{ cm}^2$
Use $\pi \approx 3.1416$ :
$\text{TSA} \approx 182 \times 3.1416 \text{ cm}^2$ $\text{TSA} \approx 571.6 \text{ cm}^2$
The curved surface area is approximately:
$\boxed{263.9 \text{ cm}^2}$
The total surface area is approximately:
$\boxed{571.6 \text{ cm}^2}$

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