How do I find the shaded area?
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This is how it looks like:
It is given that the area of the shaded region is $35 cm^2$.
All of my attempts so far ended up in a two-variable equation in terms of $r_1$ and $r_2$ (the radii of the larger circle and smaller circle respectively).
So, how do I find the area enclosed between the two circles, that is, the area of the larger circle minus the area of the smaller circle?
geometry trigonometry circle area
asked Nov 17 at 21:21
Wais Kamal
1206
add a comment |
up vote
0
down vote
favorite
This is how it looks like:
It is given that the area of the shaded region is $35 cm^2$.
All of my attempts so far ended up in a two-variable equation in terms of $r_1$ and $r_2$ (the radii of the larger circle and smaller circle respectively).
So, how do I find the area enclosed between the two circles, that is, the area of the larger circle minus the area of the smaller circle?
geometry trigonometry circle area
asked Nov 17 at 21:21
Wais Kamal
1206
No, I mean the area between the smaller circle and larger circle, excluding all other shapes.
– Wais Kamal
Nov 17 at 21:51
1
Then the hint becomes $frac12(r_1^2-r_2^2) = 35 implies pi(r_1^2-r_2^2) = ?$ which is essentially what Manika's answer does.
– achille hui
Nov 17 at 21:53
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
This is how it looks like:
It is given that the area of the shaded region is $35 cm^2$.
All of my attempts so far ended up in a two-variable equation in terms of $r_1$ and $r_2$ (the radii of the larger circle and smaller circle respectively).
So, how do I find the area enclosed between the two circles, that is, the area of the larger circle minus the area of the smaller circle?
geometry trigonometry circle area
asked Nov 17 at 21:21
Wais Kamal
1206
This is how it looks like:
It is given that the area of the shaded region is $35 cm^2$.
All of my attempts so far ended up in a two-variable equation in terms of $r_1$ and $r_2$ (the radii of the larger circle and smaller circle respectively).
So, how do I find the area enclosed between the two circles, that is, the area of the larger circle minus the area of the smaller circle?
geometry trigonometry circle area
geometry trigonometry circle area
asked Nov 17 at 21:21
Wais Kamal
1206
asked Nov 17 at 21:21
Wais Kamal
1206
asked Nov 17 at 21:21
Wais Kamal
1206
asked Nov 17 at 21:21
Wais Kamal
1206
asked Nov 17 at 21:21
Wais Kamal
1206
1206
No, I mean the area between the smaller circle and larger circle, excluding all other shapes.
– Wais Kamal
Nov 17 at 21:51
1
Then the hint becomes $frac12(r_1^2-r_2^2) = 35 implies pi(r_1^2-r_2^2) = ?$ which is essentially what Manika's answer does.
– achille hui
Nov 17 at 21:53
add a comment |
No, I mean the area between the smaller circle and larger circle, excluding all other shapes.
– Wais Kamal
Nov 17 at 21:51
1
Then the hint becomes $frac12(r_1^2-r_2^2) = 35 implies pi(r_1^2-r_2^2) = ?$ which is essentially what Manika's answer does.
– achille hui
Nov 17 at 21:53
No, I mean the area between the smaller circle and larger circle, excluding all other shapes.
– Wais Kamal
Nov 17 at 21:51
No, I mean the area between the smaller circle and larger circle, excluding all other shapes.
– Wais Kamal
Nov 17 at 21:51
1
1
Then the hint becomes $frac12(r_1^2-r_2^2) = 35 implies pi(r_1^2-r_2^2) = ?$ which is essentially what Manika's answer does.
– achille hui
Nov 17 at 21:53
Then the hint becomes $frac12(r_1^2-r_2^2) = 35 implies pi(r_1^2-r_2^2) = ?$ which is essentially what Manika's answer does.
– achille hui
Nov 17 at 21:53
add a comment |
1 Answer
1
active
oldest
votes
up vote
3
down vote
accepted
Say $R_s$ is the radius of small circle and $R_b$ is the radius of big one, then
- What you need to find is $S = pi*(R_{b}^2 - R_{s}^2)$
- What you already know is $0.5R_b^2 - 0.5R_s^2 = 0.5(R_b^2 - R_s^2) = 35$ (subtracting the areas of triangles)
From (2) you just find, that $R_b^2 - R_s^2 = 70$ and then substituting it into (1) you get $70pi$
answered Nov 17 at 21:38
Makina
1,006113
Never thought it is that simple, thanks a lot dude :)
– Wais Kamal
Nov 17 at 21:54
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Say $R_s$ is the radius of small circle and $R_b$ is the radius of big one, then
- What you need to find is $S = pi*(R_{b}^2 - R_{s}^2)$
- What you already know is $0.5R_b^2 - 0.5R_s^2 = 0.5(R_b^2 - R_s^2) = 35$ (subtracting the areas of triangles)
From (2) you just find, that $R_b^2 - R_s^2 = 70$ and then substituting it into (1) you get $70pi$
answered Nov 17 at 21:38
Makina
1,006113
Never thought it is that simple, thanks a lot dude :)
– Wais Kamal
Nov 17 at 21:54
add a comment |
up vote
3
down vote
accepted
Say $R_s$ is the radius of small circle and $R_b$ is the radius of big one, then
- What you need to find is $S = pi*(R_{b}^2 - R_{s}^2)$
- What you already know is $0.5R_b^2 - 0.5R_s^2 = 0.5(R_b^2 - R_s^2) = 35$ (subtracting the areas of triangles)
From (2) you just find, that $R_b^2 - R_s^2 = 70$ and then substituting it into (1) you get $70pi$
answered Nov 17 at 21:38
Makina
1,006113
Never thought it is that simple, thanks a lot dude :)
– Wais Kamal
Nov 17 at 21:54
add a comment |
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Say $R_s$ is the radius of small circle and $R_b$ is the radius of big one, then
- What you need to find is $S = pi*(R_{b}^2 - R_{s}^2)$
- What you already know is $0.5R_b^2 - 0.5R_s^2 = 0.5(R_b^2 - R_s^2) = 35$ (subtracting the areas of triangles)
From (2) you just find, that $R_b^2 - R_s^2 = 70$ and then substituting it into (1) you get $70pi$
answered Nov 17 at 21:38
Makina
1,006113
Say $R_s$ is the radius of small circle and $R_b$ is the radius of big one, then
- What you need to find is $S = pi*(R_{b}^2 - R_{s}^2)$
- What you already know is $0.5R_b^2 - 0.5R_s^2 = 0.5(R_b^2 - R_s^2) = 35$ (subtracting the areas of triangles)
From (2) you just find, that $R_b^2 - R_s^2 = 70$ and then substituting it into (1) you get $70pi$
answered Nov 17 at 21:38
Makina
1,006113
answered Nov 17 at 21:38
Makina
1,006113
answered Nov 17 at 21:38
Makina
1,006113
answered Nov 17 at 21:38
Makina
1,006113
1,006113
Never thought it is that simple, thanks a lot dude :)
– Wais Kamal
Nov 17 at 21:54
add a comment |
Never thought it is that simple, thanks a lot dude :)
– Wais Kamal
Nov 17 at 21:54
Never thought it is that simple, thanks a lot dude :)
– Wais Kamal
Nov 17 at 21:54
Never thought it is that simple, thanks a lot dude :)
– Wais Kamal
Nov 17 at 21:54
add a comment |
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No, I mean the area between the smaller circle and larger circle, excluding all other shapes.
– Wais Kamal
Nov 17 at 21:51
1
Then the hint becomes $frac12(r_1^2-r_2^2) = 35 implies pi(r_1^2-r_2^2) = ?$ which is essentially what Manika's answer does.
– achille hui
Nov 17 at 21:53