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3 years ago

In a circle, a 90° sector has an area of 36π in2. What is the radius of this circle?

Mathematics

2 answers:

34kurt3 years ago

6 0

Answer:

r = 12 in

Step-by-step explanation:

$A = \frac{1}{4} r^{2} \pi \\\\r = \sqrt{\frac{4A}{\pi } } = \sqrt{\frac{4 * 36\pi }{\pi } } = 2 * 6 = 12\ in$

mamaluj [8]3 years ago

4 0

Answer:

r = 12 in

Step-by-step explanation:

recall that a full circle is represented by a sector that is 360°

in our case, the given sector is 90°

Hence our sector is 90° / 360° = 1/4 of a circle

It is also given that our 90° sector (which we now know is 1/4 of a circle) has an area of 36π in² and recall that the area of a full circle is πr² (where r is the radius).

Hence,

πr² = 4 x area of 90° sector

πr² = 4 x 36π

πr² = 144π (divide both sides by π)

r² = 144

r = √144

r = 12 in

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What is the surface area of the right prism given below?

posledela

Answer: Option D.

Step-by-step explanation:

You can calculate the surface area of this right prism by adding the area of its faces.

You can observe that the faces of the right prism are: Three different rectangles and two equal triangles.

The formula for calculate the area of a rectangle is:

$A=lw$

Where "l" is the lenght and "w" is the width.

The formula for calculate the area of a triangle is:

$A=\frac{bh}{2}$

Where "b" is the base and "h" is the height.

You can observe that the hypotenuse of the each triangle is the width of one of the larger rectangle, then , you can find its value with the Pythagorean Theorem:

$a=\sqrt{b^2+c^2}$

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

Then, this is:

$a=\sqrt{(8units)^2+(15units)^2}=17units$

Therefore, you can add the areas of the faces to find the surface area of the right prism (Since the triangles are equal, you can multiply the area of one of them by 2). This is:

$SA=(10units)(8units)+(15units)(10units)+(17units)(10units)+2(\frac{(15units)(8units)}{2})\\\\SA=520units^2$

5 0

3 years ago

Read 2 more answers

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zavuch27 [327]

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3 years ago

Anyone good at explaining surface area and volume in 9th grade geometry ?

mario62 [17]

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3 years ago

If joe has12 checkers and 5/6 of them are red how many are red

natta225 [31]

Given:

The number of checkers is 12.

The number of red is 5/6 times of 12.

Multiply 5/6 and 12 to find the number of red.