How to find the length of an arc - GRE Quantitative Reasoning

length of an arc = (degrees * 2_πr)/360 = (50 * 2_π * 10)/360 = 25_π_/9

Let's compute each quantity.

Quantity A

This is a little bit more difficult than quantity B. It requires us to compute an arc length, for the ant does not walk around the whole pizza; however, this is not very hard. What we know is that the ant walks around , or , of the pizza.

Now, we know the circumference of a circle is or

For our example, let's use the latter. Since , we know:

However, our ant walks around only part of this, namely:

Quantity B

This is really just a matter of computing the circumference of the circle. For our value, we know this to be:

Now, we can compare these by taking quantity A and reducing the fraction to be . Thus, we know that Quantity B is larger than Quantity A.

The perimeter of a given pie-piece will be equal to 2 radii plus the outer arc (which is a percentage of the circumference). For our piece, this arc will be 40/360 or 1/9 of the circumference. If the area is 361π, this means πr2 = 361 and that the radius is 19. The total circumference is therefore 2 * 19 * π or 38π.

The total perimeter of the pie piece is therefore 2 * r + (1 / 9) * c = 2 * 19 + (1/9) * 38π = 38 + 38π/9

length of an arc = (degrees * 2_πr)/360 = (50 * 2_π * 10)/360 = 25_π_/9

Let's compute each quantity.

Quantity A

This is a little bit more difficult than quantity B. It requires us to compute an arc length, for the ant does not walk around the whole pizza; however, this is not very hard. What we know is that the ant walks around , or , of the pizza.

Now, we know the circumference of a circle is or

For our example, let's use the latter. Since , we know:

However, our ant walks around only part of this, namely:

Quantity B

This is really just a matter of computing the circumference of the circle. For our value, we know this to be:

Now, we can compare these by taking quantity A and reducing the fraction to be . Thus, we know that Quantity B is larger than Quantity A.

The perimeter of a given pie-piece will be equal to 2 radii plus the outer arc (which is a percentage of the circumference). For our piece, this arc will be 40/360 or 1/9 of the circumference. If the area is 361π, this means πr2 = 361 and that the radius is 19. The total circumference is therefore 2 * 19 * π or 38π.

The total perimeter of the pie piece is therefore 2 * r + (1 / 9) * c = 2 * 19 + (1/9) * 38π = 38 + 38π/9

length of an arc = (degrees * 2_πr)/360 = (50 * 2_π * 10)/360 = 25_π_/9

Let's compute each quantity.

Quantity A

This is a little bit more difficult than quantity B. It requires us to compute an arc length, for the ant does not walk around the whole pizza; however, this is not very hard. What we know is that the ant walks around , or , of the pizza.

Now, we know the circumference of a circle is or

For our example, let's use the latter. Since , we know:

However, our ant walks around only part of this, namely:

Quantity B

This is really just a matter of computing the circumference of the circle. For our value, we know this to be:

Now, we can compare these by taking quantity A and reducing the fraction to be . Thus, we know that Quantity B is larger than Quantity A.

The perimeter of a given pie-piece will be equal to 2 radii plus the outer arc (which is a percentage of the circumference). For our piece, this arc will be 40/360 or 1/9 of the circumference. If the area is 361π, this means πr2 = 361 and that the radius is 19. The total circumference is therefore 2 * 19 * π or 38π.

The total perimeter of the pie piece is therefore 2 * r + (1 / 9) * c = 2 * 19 + (1/9) * 38π = 38 + 38π/9

length of an arc = (degrees * 2_πr)/360 = (50 * 2_π * 10)/360 = 25_π_/9

Let's compute each quantity.

Quantity A

This is a little bit more difficult than quantity B. It requires us to compute an arc length, for the ant does not walk around the whole pizza; however, this is not very hard. What we know is that the ant walks around , or , of the pizza.

Now, we know the circumference of a circle is or

For our example, let's use the latter. Since , we know:

However, our ant walks around only part of this, namely:

Quantity B

This is really just a matter of computing the circumference of the circle. For our value, we know this to be:

Now, we can compare these by taking quantity A and reducing the fraction to be . Thus, we know that Quantity B is larger than Quantity A.

The perimeter of a given pie-piece will be equal to 2 radii plus the outer arc (which is a percentage of the circumference). For our piece, this arc will be 40/360 or 1/9 of the circumference. If the area is 361π, this means πr2 = 361 and that the radius is 19. The total circumference is therefore 2 * 19 * π or 38π.

The total perimeter of the pie piece is therefore 2 * r + (1 / 9) * c = 2 * 19 + (1/9) * 38π = 38 + 38π/9

length of an arc = (degrees * 2_πr)/360 = (50 * 2_π * 10)/360 = 25_π_/9

Let's compute each quantity.

Quantity A

This is a little bit more difficult than quantity B. It requires us to compute an arc length, for the ant does not walk around the whole pizza; however, this is not very hard. What we know is that the ant walks around , or , of the pizza.

Now, we know the circumference of a circle is or

For our example, let's use the latter. Since , we know:

However, our ant walks around only part of this, namely:

Quantity B

This is really just a matter of computing the circumference of the circle. For our value, we know this to be:

Now, we can compare these by taking quantity A and reducing the fraction to be . Thus, we know that Quantity B is larger than Quantity A.

The perimeter of a given pie-piece will be equal to 2 radii plus the outer arc (which is a percentage of the circumference). For our piece, this arc will be 40/360 or 1/9 of the circumference. If the area is 361π, this means πr2 = 361 and that the radius is 19. The total circumference is therefore 2 * 19 * π or 38π.

The total perimeter of the pie piece is therefore 2 * r + (1 / 9) * c = 2 * 19 + (1/9) * 38π = 38 + 38π/9

length of an arc = (degrees * 2_πr)/360 = (50 * 2_π * 10)/360 = 25_π_/9

Let's compute each quantity.

Quantity A

This is a little bit more difficult than quantity B. It requires us to compute an arc length, for the ant does not walk around the whole pizza; however, this is not very hard. What we know is that the ant walks around , or , of the pizza.

Now, we know the circumference of a circle is or

For our example, let's use the latter. Since , we know:

However, our ant walks around only part of this, namely:

Quantity B

This is really just a matter of computing the circumference of the circle. For our value, we know this to be:

Now, we can compare these by taking quantity A and reducing the fraction to be . Thus, we know that Quantity B is larger than Quantity A.

The perimeter of a given pie-piece will be equal to 2 radii plus the outer arc (which is a percentage of the circumference). For our piece, this arc will be 40/360 or 1/9 of the circumference. If the area is 361π, this means πr2 = 361 and that the radius is 19. The total circumference is therefore 2 * 19 * π or 38π.

The total perimeter of the pie piece is therefore 2 * r + (1 / 9) * c = 2 * 19 + (1/9) * 38π = 38 + 38π/9

length of an arc = (degrees * 2_πr)/360 = (50 * 2_π * 10)/360 = 25_π_/9