Question

a circle has a diameter of 10 m. what is its circumference?
31.4 m
15.7 m
78.5 m
62.8 m
a shape is dilated by a scale factor of 3. the original perimeter was 12 cm. new perimeter?
36 cm
9 cm
15 cm
27 cm

Explanation:

Step1: Calculate the circumference of the circle

The formula for the circumference of a circle is \(C = \pi d\), where \(d\) is the diameter. Given \(d = 10\) m and taking \(\pi\approx3.14\), we have \(C=3.14\times10 = 31.4\) m.

Step2: Calculate the new perimeter after dilation

When a shape is dilated by a scale factor \(k\), the new perimeter \(P_{new}\) is related to the original perimeter \(P_{old}\) by the formula \(P_{new}=k\times P_{old}\). Here, \(k = 3\) and \(P_{old}=12\) cm. So \(P_{new}=3\times12=36\) cm.

Answer:

First question: 31.4 m
Second question: 36 cm