QuestionCalculate the circumference and area of a circle with diameter $6 \mathrm{yd}$ using $\pi \approx 3.14$ . Include units.

Studdy Solution

STEP 1

Assumptions1. The diameter of the circle is6 yards. The value of $\pi$ is3.143. The formulas for circumference and area of a circle are $C = \pi d$ and A = \pi r^ respectively, where $d$ is the diameter and $r$ is the radius of the circle.

STEP 2

First, we need to find the radius of the circle. The radius is half the diameter.
$r = \frac{d}{2}$

STEP 3

Now, plug in the given value for the diameter to calculate the radius.
$r = \frac{6 \, \mathrm{yd}}{2}$

STEP 4

Calculate the radius.
$r = \frac{6 \, \mathrm{yd}}{2} =3 \, \mathrm{yd}$

STEP 5

Now that we have the radius, we can find the circumference of the circle using the formula $C = \pi d$ .
$C = \pi d$

STEP 6

Plug in the values for $\pi$ and the diameter to calculate the circumference.
$C =3.14 \times6 \, \mathrm{yd}$

STEP 7

Calculate the circumference.
$C =3.14 \times6 \, \mathrm{yd} =18.84 \, \mathrm{yd}$

STEP 8

Now that we have the circumference, we can find the area of the circle using the formula $A = \pi r^2$ .
$A = \pi r^2$

STEP 9

Plug in the values for $\pi$ and the radius to calculate the area.
$A =3.14 \times (3 \, \mathrm{yd})^2$

STEP 10

Calculate the area.
$A =3.14 \times (3 \, \mathrm{yd})^2 =28.26 \, \mathrm{yd}^2$ The circumference of the circle is $18.84 \, \mathrm{yd}$ and the area is $28.26 \, \mathrm{yd}^2$ .

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QuestionCalculate the circumference and area of a circle with diameter $6 \mathrm{yd}$ using $\pi \approx 3.14$ . Include units.

Studdy Solution

STEP 1

Assumptions1. The diameter of the circle is6 yards. The value of $\pi$ is3.143. The formulas for circumference and area of a circle are $C = \pi d$ and A = \pi r^ respectively, where $d$ is the diameter and $r$ is the radius of the circle.

STEP 2

First, we need to find the radius of the circle. The radius is half the diameter.
$r = \frac{d}{2}$

STEP 3

Now, plug in the given value for the diameter to calculate the radius.
$r = \frac{6 \, \mathrm{yd}}{2}$

STEP 4

Calculate the radius.
$r = \frac{6 \, \mathrm{yd}}{2} =3 \, \mathrm{yd}$

STEP 5

Now that we have the radius, we can find the circumference of the circle using the formula $C = \pi d$ .
$C = \pi d$

STEP 6

Plug in the values for $\pi$ and the diameter to calculate the circumference.
$C =3.14 \times6 \, \mathrm{yd}$

STEP 7

Calculate the circumference.
$C =3.14 \times6 \, \mathrm{yd} =18.84 \, \mathrm{yd}$

STEP 8

Now that we have the circumference, we can find the area of the circle using the formula $A = \pi r^2$ .
$A = \pi r^2$

STEP 9

Plug in the values for $\pi$ and the radius to calculate the area.
$A =3.14 \times (3 \, \mathrm{yd})^2$

STEP 10

Calculate the area.
$A =3.14 \times (3 \, \mathrm{yd})^2 =28.26 \, \mathrm{yd}^2$ The circumference of the circle is $18.84 \, \mathrm{yd}$ and the area is $28.26 \, \mathrm{yd}^2$ .

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QuestionCalculate the circumference and area of a circle with diameter 6yd6 \mathrm{yd}6yd using π≈3.14\pi \approx 3.14π≈3.14. Include units.

Studdy Solution

STEP 1

Assumptions1. The diameter of the circle is6 yards. The value of π\piπ is3.143. The formulas for circumference and area of a circle are C=πdC = \pi dC=πd and A = \pi r^ respectively, where ddd is the diameter and rrr is the radius of the circle.

STEP 2

First, we need to find the radius of the circle. The radius is half the diameter.r=d2r = \frac{d}{2}r=2d​

STEP 3

Now, plug in the given value for the diameter to calculate the radius.r=6 yd2r = \frac{6 \, \mathrm{yd}}{2}r=26yd​

STEP 4

Calculate the radius.r=6 yd2=3 ydr = \frac{6 \, \mathrm{yd}}{2} =3 \, \mathrm{yd}r=26yd​=3yd

STEP 5

Now that we have the radius, we can find the circumference of the circle using the formula C=πdC = \pi dC=πd.C=πdC = \pi dC=πd

STEP 6

Plug in the values for π\piπ and the diameter to calculate the circumference.C=3.14×6 ydC =3.14 \times6 \, \mathrm{yd}C=3.14×6yd

STEP 7

Calculate the circumference.C=3.14×6 yd=18.84 ydC =3.14 \times6 \, \mathrm{yd} =18.84 \, \mathrm{yd}C=3.14×6yd=18.84yd

STEP 8

Now that we have the circumference, we can find the area of the circle using the formula A=πr2A = \pi r^2A=πr2.A=πr2A = \pi r^2A=πr2

STEP 9

Plug in the values for π\piπ and the radius to calculate the area.A=3.14×(3 yd)2A =3.14 \times (3 \, \mathrm{yd})^2A=3.14×(3yd)2

STEP 10

Calculate the area.A=3.14×(3 yd)2=28.26 yd2A =3.14 \times (3 \, \mathrm{yd})^2 =28.26 \, \mathrm{yd}^2A=3.14×(3yd)2=28.26yd2The circumference of the circle is 18.84 yd18.84 \, \mathrm{yd}18.84yd and the area is 28.26 yd228.26 \, \mathrm{yd}^228.26yd2.

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QuestionCalculate the circumference and area of a circle with diameter $6 \mathrm{yd}$ using $\pi \approx 3.14$ . Include units.

Assumptions1. The diameter of the circle is6 yards. The value of $\pi$ is3.143. The formulas for circumference and area of a circle are $C = \pi d$ and A = \pi r^ respectively, where $d$ is the diameter and $r$ is the radius of the circle.

First, we need to find the radius of the circle. The radius is half the diameter.
$r = \frac{d}{2}$

Now, plug in the given value for the diameter to calculate the radius.
$r = \frac{6 \, \mathrm{yd}}{2}$

Calculate the radius.
$r = \frac{6 \, \mathrm{yd}}{2} =3 \, \mathrm{yd}$

Now that we have the radius, we can find the circumference of the circle using the formula $C = \pi d$ .
$C = \pi d$

Plug in the values for $\pi$ and the diameter to calculate the circumference.
$C =3.14 \times6 \, \mathrm{yd}$

Calculate the circumference.
$C =3.14 \times6 \, \mathrm{yd} =18.84 \, \mathrm{yd}$

Now that we have the circumference, we can find the area of the circle using the formula $A = \pi r^2$ .
$A = \pi r^2$

Plug in the values for $\pi$ and the radius to calculate the area.
$A =3.14 \times (3 \, \mathrm{yd})^2$

Calculate the area.
$A =3.14 \times (3 \, \mathrm{yd})^2 =28.26 \, \mathrm{yd}^2$ The circumference of the circle is $18.84 \, \mathrm{yd}$ and the area is $28.26 \, \mathrm{yd}^2$ .