Question

9-The diameter of circle B is 50% longer than the diameter of circle A.If we
divide the area of circle B by the area of circle A, the result is:
(a) 1.5
(b) 1.25
(c)2.25
(d)None of the previous

Answer 1

Step-by-step explanation:

Let the diameter of circle A be

�

d. The diameter of circle B is

1.5

�

1.5d (50% longer).

The area of a circle is proportional to the square of its diameter. So, the ratio of the areas of B to A is

(1.5d)^2 /d^2.

Simplifying, we get

2.25

2.25, which corresponds to option (c). Therefore, the result is:

(c) 2.25

Answer 2

Answer:

(c) 2.25

Step-by-step explanation:

Let d be the diameter of circle A.

Given that the diameter of circle B is 50% longer that the diameter of circle A, then:

$\textsf{Diameter of circle B} = d + 50\%\;\textsf{of}\;d\\\\\textsf{Diameter of circle B} =d+0.5d\\\\\textsf{Diameter of circle B} =1.5d$

So the diameter of circle B is 1.5d.

The area of a circle is given by the formula A = πr², where r is the radius.

Since the radius of a circle is half its diameter, the radii of the circles are:

$\textsf{Radius of circle A} = \dfrac{d}{2}=0.5d\\\\\\\textsf{Radius of circle B} = \dfrac{1.5d}{2}=0.75d$

If we substitute the radii of into the area formula we get:

$\textsf{Area of circle A} = \pi \cdot (0.5d)^2=0.25d^2\pi\\\\\\\textsf{Area of circle B} = \pi \cdot (0.75d)^2=0.5625d^2\pi$

Now, divide the expression for the area of circle B by the expression for the area of circle A:

$\dfrac{0.5625d^2\pi}{0.25d^2\pi}$

Cancel the common factor d²π and simplify:

$\dfrac{0.5625}{0.25}=2.25$

Therefore, if we divide the area of circle B by the area of circle A, given that the diameter of circle B is 50% longer than the diameter of circle A, the result is:

$\LARGE\boxed{\boxed{2.25}}$