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Rainbow [258]
3 years ago
9

Find the radius of a circle given that the area is three times its circumference

Mathematics
1 answer:
lbvjy [14]3 years ago
5 0

Answer:

Radius of the circle = 6 units

Step-by-step explanation:

Let the radius of the circle be r

According to the given condition:

Area of the circle = 3 times the circumference of the circle

\therefore \pi r^2 =3\times 2\pi r\\\therefore r^2 = \frac{3\times 2\pi r}{\pi}\\\therefore r^2 = 3\times 2r\\\therefore r = 6\: units\\

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7 0
3 years ago
The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm.
Nat2105 [25]

Answer:

A) Maximum error = 170.32 cm³

B)Relative error = 0.0575

Step-by-step explanation:

A) Formula for circumference is: C = 2πr

Differentiating with respect to r, we have;

dC/dr = 2π

r is small, so we can write;

ΔC/Δr = 2π

So, Δr = ΔC/2π

We are told that ΔC = 0.5.

Thus; Δr = 0.5/2π = 0.25/π

Now, formula for Volume of a sphere is;

V(r) = (4/3)πr³

Differentiating with respect to r, we have;

dV/dr = 4πr²

Again, r is small, so we can write;

ΔS/Δr = 4πr²

ΔV = 4πr² × Δr

Rewriting, we have;

ΔV = ((2πr)²/π) × Δr

Since C = 2πr, we now have;

ΔV = (C²/π)Δr

ΔV will be maximum when Δr is maximum

Thus, ΔV = (C²/π) × 0.25/π

C = 82 cm

Thus;

ΔV = (82²/π) × 0.25/π

ΔV = 170.32 cm³

B) Formula for relative error = ΔV/V

Relative error = 170.32/((4/3)πr³)

Relative error = 170.32/((4/3)C³/8π³)

Relative errror = 170.32/((4/3)82³/8π³)

Relative error = 170.32/2963.744

Relative error = 0.0575

3 0
3 years ago
If BE is parallel to CD, the. The value of x is: <br><br> A. 10<br><br> B. 6<br><br> C. 9
sveta [45]
Corresponding sides have the same ratio, so
  x/15 = 12/(12+8) = 3/5
  x = 15*3/5
  x = 9
4 0
3 years ago
Which segment is both a chord and diameter segment____ . AO AE BC B
alexandr402 [8]

Answer:

Answer is BD

Step-by-step explanation:

7 0
3 years ago
Which equation calculates the number of 1/3-foot pieces that can be cut from a piece of
harina [27]

Answer:

7:\dfrac{1}{3}=21 pieces

Step-by-step explanation:

Suppose you have a 7 feet long wood.

You need to find how many \frac{1}{3}-foot pieces can be cut from this wood.

To find this number of pieces, you have to divide the whole length of the wood by the length of one piece:

7:\dfrac{1}{3}=\dfrac{7}{1}\cdot \dfrac{3}{1}=21

8 0
3 years ago
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