Question

The ratio of the diameters of two circles is 3:4. Find the ratio of their circu​

Answer 1

Answer:

Explanation:

When comparing 2 similar figures, the ratio of any corresponding lengths will have the same ratio. So the ratio of the circumferences would also be 3:4. 

However, the ratio of the circle's areas would be those numbers squared, so the ratio of their areas would be 3²:4² = 9:16. 

If you were comparing one rectangle to a similar rectangle, if their lengths had the ratio of 3:4, then their widths, their perimeters and their diagonals would all have the ratio 3:4, but their areas would have the ratio 9:16. 

If you went to 3 dimensional figures like a rectangular prism, if their lengths had the ratio of 3:4, then their widths, their heights, their corresponding perimeters and their diagonals would all have the ratio 3:4, but their surface areas would have the ratio 9:16. Their volumes would have the original side ratio cubed, 3³:4³ = 27:64. 

Answer 2

$\huge\mathbb{\blue{QUESTION-}}$

The ratio of the diameters of two circles is 3:4. Find the ratio of their circumference of circle .

$\huge\mathbb{\blue{SOLUTION-}}$

$\large\underline{\underline{\sf Given:}}$

• Ratio of diameter ${\sf (d_1:d_2)}$ = 3:4

$\large\underline{\underline{\sf To\:Find:}}$

• Circumference of circle ${\sf (C_1:C_2)}$

Diameter = Radius / 2

$\implies{\sf \blue{ r_1=\dfrac{3}{2}}}$

$\implies{\sf r_2=\dfrac{4}{2} }$

$\implies{\sf \blue{ r_2=2}}$

❏ Circumference ( C ) = 2πr

$\implies{\sf C_1=2π×\dfrac{3}{2} }$

$\implies{\bf \blue{C_1=3π }}$

$\implies{\sf C_2=2π×2}$

$\implies{\bf \blue{C_2=4π}}$

❏ Ratio of Circumference

$\implies{\sf \dfrac{C_1}{C_2}=\dfrac{3π}{4π}}$

$\implies{\bf \red{\dfrac{C_1}{C_2}=\dfrac{3}{4}}}$

$\huge\mathbb{\blue{ANSWER-}}$

Ratio of Circumference is ${\bf \red{C_1:C_2=3:4}}$