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2 years ago

The circumference of a cirlcle is 6π inches. What is the area of the cirlce?

Mathematics

2 answers:

dsp732 years ago

8 0

The correct answer is B.

Start from the equation for the circumference and solve it for the radius:

$C = 2\pi r \implies r = \frac{C}{2\pi}$

So, the radius of the circumference is

$\frac{6\pi}{2\pi} = 3$ inches

Once the radius in known, you can plug it in the formula for the area:

$A = \pir^2 = 9\pi$ squared inches.

Dimas [21]2 years ago

6 0

Answer:the answer would be A

Step-by-step explanation:

C= 2πr

6π=2πr

——/—-

2π. 2π

3=r

A = 3π inches squared

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A cone has a slant length of 10 and a diameter of 8. Height is unknown.

patriot [66]

Answer: 153.56

Step-by-step explanation:

Hi, to answer this question we have to apply the next formulas:

Volume of a cone: 1/3 π r² h

Where r is the radius and h is the height (unknown)

Diameter = r x 2

8 = 2r

8/2 =r

r = 4

Before calculating the volume we have to apply the Pythagorean Theorem to find h. (where the slant is the hypotenuse and h and r are the sides of the triangle)

10 ² = h² + 4²

Solving for h

100 = h² + 16

100-16 = h²

84= h²

√84 =h

9.16= h

Back on the volume formula:

V= 1/3 π r² h

V =1/3 π 4² (9.16) =153.56

6 0

3 years ago

You have just bought a new television and it has an aspect ratio of 16:9. The screen on the television is 65 inches. What is the

dem82 [27]

Answer:

Width of T.V. is 21.94 inches Height is 39 inches and area is 855.66 square inch.

Step-by-step explanation:

When we buy an electronic item like T.V or Blue Ray aspect ratio is the term which is used by the salesmen or technicians. Aspect ratio is actually the ratio of length and breadth of the screen of a device or ration of width and height.

In this question aspect ratio of television is given as 16:9

This can be written as $\frac{W}{H}=\frac{16}{9}$ or $W=\frac{16}{9} H$

Screen of the T.V. is 65 inch which is the diagonal length of the screen.

We know from pythagoras theorem in a right angle triangle

$(diagonal)^{2}=(base)^2+(height)^2$

$(65)^2=(Base)^2+(height)^2$

$(65)^2= W^2+H^2 = (\frac{16}{9}H)^2+H^2$

$(65)= \sqrt{\frac{16}{9}H^2+H^2}\\ 65=H\sqrt{\frac{16}{9}+1}\\ 65=H\sqrt{\frac{25}{9}}\\ 65=\frac{5}{3}H\\ H=39 inches$

Now height of the T.V.will be

$\frac{W}{H}=\frac{16}{9} \\\\\frac{H}{W}=\frac{9}{16}\\ H=\frac{9}{16}W = (\frac{9}{16})39= 21.94 Inches$

now area of the T.V.=W×H=39×21.94=855.66 square inch

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