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The figure below shows a rope that circles the Earth. The radius of the Earth is 6371 kilometers.
Assuming the rope makes a perfect circle, what is the length of this rope?
Give your answer in terms of pi.

The figure below shows a rope that circles the Earth. The radius of the Earth is $6371$ kilometers. $\newline$ Assuming the rope makes a perfect circle, what is the length of this rope? $\newline$ Give your answer in terms of pi. $\newline$ $\square$ kilometers

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Scale drawings: scale factor word problems

Full solution

Q. The figure below shows a rope that circles the Earth. The radius of the Earth is

6371

kilometers.

\newline

Assuming the rope makes a perfect circle, what is the length of this rope?

\newline

Give your answer in terms of pi.

\newline

\square

kilometers

Calculate Circumference Formula: To find the length of the rope, we need to calculate the circumference of the Earth using the formula $C = 2 \times \pi \times r$ , where $C$ is the circumference and $r$ is the radius.
Plug in Radius: Plug in the radius of the Earth into the formula: $C = 2 \times \pi \times 6371$ km.
Perform Multiplication: Perform the multiplication to get the length of the rope: $C = 2 \times \pi \times 6371 \, \text{km} = 12742 \times \pi \, \text{km}.$
Check Calculation: Check the calculation for any errors. The formula and numbers look correct.

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Question

10\text{-kg}

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Question

10-\mathrm{kg}

bucket is lifted from the ground to a height of

14

m at a constant speed with a rope that weighs

0.6 \mathrm{~kg} / \mathrm{m}

. Initially the bucket contains

42

kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the

14-\mathrm{m}

level. How much work is done? (Use

9.8 \mathrm{~m} / \mathrm{s}^{2}

\newline

Show how to approximate the required work (in J) by a Riemann sum. (Let

x

be the height in meters above the ground. Enter

x_{i}^{* *}

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\newline

\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(\boxed{98+35.28 x_{i}}\right) \Delta x

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Evaluate the integral (in J). (Round your answer to the nearest integer.)

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