Any clue on how to do this?

Mathematics

1 answer:

balu736 [363]3 years ago

6 0

First thing you need to know is the measure of the central angle. It is the same as the measure of the arc it intercepts, which is 100 degrees. The formula now is this for the area of a sector: $A= \frac{100}{360} * \pi (16)^{2}$ which comes out to $\frac{640 \pi }{9}$ . If you multiply the pi in you'll get 223.4 or thereabouts.

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A circle has a radius of 9 inches. The Radius is multiplied by 2/3 to form a second circle. How is the ratio of the areas relate

liraira [26]

Answer:

$\frac {(Area\ of\ first\ circle) }{(Area\ of\ second\ circle)} = \frac{81}{36} = (\frac{r_{1} }{r_{2}}) ^{2}$

The above expression shows that ratios of the areas of the circles are equal to the square of the ratio of their radii.

Step-by-step explanation:

Radius of first circle $(r_{1})$ = 9 inches

Area of first circle = $\pi r_{1} ^{2}$

Area of first circle = 9 × 9 × π = 81 π

Now, since the radius is multiplied by 2/3 for from a new circle.

∴ Radius of the second circle = $9 \times \frac{2}{3} = 6\ inches$

Area of second circle = $\pi r_{2} ^{2}$

Area of second circle = 6 × 6 × π = 36 π

Now,

$\frac {(Area\ of\ first\ circle) }{(Area\ of\ second\ circle)} = \frac{81\pi }{36\pi }$

$\frac {(Area\ of\ first\ circle) }{(Area\ of\ second\ circle)} = \frac{81}{36} = (\frac{9}{6}) ^{2} = (\frac{r_{1} }{r_{2}}) ^{2}$

∵ $(r_{1})$ = 9 inches and $(r_{2})$ = 6 inches

The above expression shows that ratios of the areas of the circles are equal to the square of the ratio of their radii. i.e., $\frac {radius\ of\ first\ circle)^{2} }{(radius\ of\ second\ circle)^{2} } = \frac {(Area\ of\ first\ circle) }{(Area\ of\ second\ circle)}$