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Question

2cm and 5 cm
Question
Find the surface area of a cylinder with a radius of 4 and a height of 3. Use 3.14 for π
.

Round your answer to the nearest tenths place.

(1 point)
Responses

87.9 cm2
87.9 cm 2

175.8 cm2
175.8 cm 2

120.3 cm2
120.3 cm 2

75.3 cm2

Answer 1

To find the surface area of a cylinder, we can use the formula:

$$\text{Surface Area}=2\pi r(h+r)$$

Where:

• $r$ is the radius,
• $h$ is the height,
• $\pi$ is approximately 3.14.

Given:

• Radius ($r$) = 4 cm
• Height ($h$) = 3 cm

Let's plug the values into the formula:

$$\text{Surface Area}=2\times 3.14\times 4\times (3+4)$$ $$=2\times 3.14\times 4\times 7$$ $$=2\times 3.14\times 28$$ $$=6.28\times 28$$ $$=176.84$$

Now rounding to the nearest tenths place:

$$176.84\approx 176.8,{\text{cm}}^2$$

However, since this value does not match any of the provided responses, let’s double-check through calculating the total surface area of the cylinder, which also involves the areas of the two circular bases.

The total surface area formula also can be split into:

$$\text{Surface Area}=2\pi r^2+2\pi rh$$

Calculating each part:

1. Area of the bases: $$2\pi r^2=2\times 3.14\times (4^2)=2\times 3.14\times 16=100.48,{\text{cm}}^2$$

2. Lateral surface area: $$2\pi rh=2\times 3.14\times 4\times 3=2\times 3.14\times 12=75.36,{\text{cm}}^2$$

3. Total surface area: Combining both parts: $$100.48+75.36=175.84,{\text{cm}}^2$$

Rounding this to the nearest tenths place gives:

$$175.8,{\text{cm}}^2$$

So, the correct response is:

175.8 cm²