Question

a cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift.

what is the approximate volume of the tube? round to the nearest whole cubic centimeter.

\\(1,005\text{ cm}^3\\)
\\(1,340\text{ cm}^3\\)
\\(3,351\text{ cm}^3\\)
\\(4,021\text{ cm}^3\\)

Explanation:

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<reasoning>

Identify the given dimensions

We are given a cylindrical cardboard tube with:

• Diameter \(d = 8\text{ cm}\)
• Height \(h = 20\text{ cm}\)

Calculate the radius of the cylinder

The radius \(r\) is half of the diameter:
\[r = \frac{d}{2} = \frac{8}{2} = 4\text{ cm}\]

Apply the cylinder volume formula

The volume \(V\) of a cylinder is calculated using the formula:
\[V = \pi r^2 h\]
Substituting our values:
\[V = \pi \cdot (4)^2 \cdot 20\]
\[V = \pi \cdot 16 \cdot 20\]
\[V = 320\pi\]

Calculate the approximate numerical value

Using the approximation \(\pi \approx 3.14159\):
\[V \approx 320 \cdot 3.14159 \approx 1005.31\text{ cm}^3\]
Rounding to the nearest whole cubic centimeter gives:
\[V \approx 1005\text{ cm}^3\]
</reasoning>

<answer>
<mcq-correct>(A) 1,005 cm³</mcq-correct>
<mcq-option>(B) 1,340 cm³</mcq-option>
<mcq-option>(C) 3,351 cm³</mcq-option>
<mcq-option>(D) 4,021 cm³</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given dimensions

We are given a cylindrical cardboard tube with:

• Diameter \(d = 8\text{ cm}\)
• Height \(h = 20\text{ cm}\)

Calculate the radius of the cylinder

The radius \(r\) is half of the diameter:
\[r = \frac{d}{2} = \frac{8}{2} = 4\text{ cm}\]

Apply the cylinder volume formula

The volume \(V\) of a cylinder is calculated using the formula:
\[V = \pi r^2 h\]
Substituting our values:
\[V = \pi \cdot (4)^2 \cdot 20\]
\[V = \pi \cdot 16 \cdot 20\]
\[V = 320\pi\]

Calculate the approximate numerical value

Using the approximation \(\pi \approx 3.14159\):
\[V \approx 320 \cdot 3.14159 \approx 1005.31\text{ cm}^3\]
Rounding to the nearest whole cubic centimeter gives:
\[V \approx 1005\text{ cm}^3\]
</reasoning>

<answer>
<mcq-correct>(A) 1,005 cm³</mcq-correct>
<mcq-option>(B) 1,340 cm³</mcq-option>
<mcq-option>(C) 3,351 cm³</mcq-option>
<mcq-option>(D) 4,021 cm³</mcq-option>
</answer>

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