Radian measure- find shaded region

Can someone confirm my working out.

So, it looks pretty straightforward to me.

Find area of the sector and triangle independently and then take the area of the triangle away from the sector.

I have rounded up and down for the 45degree angle in terms of the radian, to justify my answer in relation to the one in the text book.

The textbook claims it’s 5.14 but I can only find it to be 5.22 or 5.04

(edited 1 year ago)

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Reply 1

emmap2003

12

I got 5.14 by leaving the 45 degrees in its exact radians form

Reply 2

old_engineer

11

Original post by KingRich

Can someone confirm my working out.

I think your main problem is rounding too early. Note also that the angle in the question is given in degrees not radians. 45 deg is one eighth of a circle, so the area of the sector is just pi(r^2)/8.

Reply 3

KingRich

OP

14

Original post by emmap2003

I got 5.14 by leaving the 45 degrees in its exact radians form

Mmm, it didn’t state exact value. This is probably why I automatically converted angle to radian decimal form and rounded up. Thanks

Reply 4

KingRich

OP

14

Original post by old_engineer

I think your main problem is rounding too early. Note also that the angle in the question is given in degrees not radians. 45 deg is one eighth of a circle, so the area of the sector is just pi(r^2)/8.

As this section focuses on
Area of arc=1/2 r² x theta(when in radian form). It’s the reason that I applied that approach.

I didn’t think as far as it being an eight of a circle but it does now give me another perspective to think from.

than you

Reply 5

mqb2766

21

Original post by KingRich

Mmm, it didn’t state exact value. This is probably why I automatically converted angle to radian decimal form and rounded up. Thanks

Do you see that to get an answer to 3 sig fig, you really need to be working to 4 sig fig and you seem to be only using 2? You need an extra sig fig because you subtract "10" (well 9) at the end so one of the digits disappears. Always work at 3 sig fig as a minimum, but here an extra one would be advisable as
pi/4 = 0.78539816339
then 0.7854 would be appropriate.

(edited 1 year ago)

Reply 6

KingRich

OP

14

Original post by mqb2766

Do you see that to get an answer to 3 sig fig, you really need to be working to 4 sig fig and you seem to be only using 2? You need an extra sig fig because you subtract "10" (well 9) at the end so one of the digits disappears. Always work at 3 sig fig as a minimum, but here an extra one would be advisable as
pi/4 = 0.78539816339
then 0.7854 would be appropriate.

Ah, okay. This would be the rule to abide by even if it doesn’t state showing the value as exactly.

Thank you

Reply 7

mqb2766

21

Original post by KingRich

Ah, okay. This would be the rule to abide by even if it doesn’t state showing the value as exactly.

Thank you

If its not an exact value, then 3 sig fig is the usual.
However, you may need to work to 4 sig fig throughout the question to round at the end. Otherwise arithmetic on the numbers (ronding errors) may affect the 3rd sig fig (or higher as per this question).
Here pi/4 would "naturally" round to 4 sig fig as its very close to the true value.

(edited 1 year ago)

Radian measure- find shaded region

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