Find (a) the diameter, (b) the radius of each circle, given the circumference as Take π = 22/7. The diameter of Venus planet is 12278 km. Find its circumference.

Understand the Problem

The question provides various exercises related to the diameter and circumference of circles, as well as calculating the ratio of circumferences and the side of a square formed with a bent wire. It requires applying formulas for circumference and diameter using the value of π, along with basic geometry.

Answer

Diameter of Venus = 12278 km, Radius = 6139 km, Circumference = 38538 km.

Steps to Solve

Find the Diameter and Radius The relationship between the diameter (d) and the radius (r) of a circle is given by: $$ r = \frac{d}{2} $$
Find the Circumference of Venus The formula for the circumference (C) of a circle is: $$ C = \pi \times d $$ Using $\pi = \frac{22}{7}$ and the diameter of Venus (d = 12278 km), we can calculate the circumference.
Substituting Values for Circumference Substitute the values into the circumference formula: $$ C = \frac{22}{7} \times 12278 $$
Performing the Calculation Calculate the right-hand side to find the circumference.

The diameter of each circle is provided in the question, so (a) is already known as 12278 km. The radius for Venus is: $$ r = \frac{12278}{2} = 6139 \text{ km} $$ The circumference of Venus is: $$ C = \frac{22}{7} \times 12278 = 38538 \text{ km} $$

More Information

The diameter and radius can help in understanding the size of the planet Venus, and the use of $\pi$ in calculating circumference shows its importance in circle measurements.

Tips

Forgetting the relationship between diameter and radius can lead to incorrect radius calculations.
Incorrectly substituting values into formulas may yield wrong circumferences.

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