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secondary 3 | E Maths
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Date Posted: 7 months ago
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This should be enough information but I'll go in-depth here.
A) If you draw the lines you'd notice that the height of AOB is 3cm. Since 8-5 is 3. 8 is derived from the radius. Next, you can find Angle AOD (D is the shortest distance between O and AB aka the height). In a right angle triangle,
sin(x) = opposite/hypotenuse, cos(x) = adjacent/hypotenuse, tan(x) = opposite/adjacent.
Here we will use cos(x). We'll get 3/8 since the adjacent of angle AOD is 3 and the hypotenuse is 8. Inverse cosine 3/8 (cos^-1 (3/8) ) will give you AOD. Multiply twice since Angle AOD and BOD are equal due to similar triangles. After that you'll get Angle AOB.
The answer should be 2.37 (3 s.f) in radians. Use the calculator value for parts b), c) and d) for accuracy
B) In this question you just need to input the formula Area = ½ x r²(∅-sin∅). Ø is the answer from part A).
The answer should be 53.7 (3 s.f) Use calculator value for parts c) and d) for accuracy.
C) In this question you just use the formula of Surface Area x Height. Surface Area is your segment area and height is 25cm.
The answer should be 1342 (nearest whole) or 1340 (3 s.f). Use calculator value for part D) for accuracy.
D) In this part you will take the volume of water found in part (C) and divide that by the surface area of the cylinder (circle area). To find the S.A of the cylinder, π(r²) where r is the radius, 8cm. Afterwards, use the calculator value of C) and divide.
Your answer should be 6.67 (3 s.f)
A) If you draw the lines you'd notice that the height of AOB is 3cm. Since 8-5 is 3. 8 is derived from the radius. Next, you can find Angle AOD (D is the shortest distance between O and AB aka the height). In a right angle triangle,
sin(x) = opposite/hypotenuse, cos(x) = adjacent/hypotenuse, tan(x) = opposite/adjacent.
Here we will use cos(x). We'll get 3/8 since the adjacent of angle AOD is 3 and the hypotenuse is 8. Inverse cosine 3/8 (cos^-1 (3/8) ) will give you AOD. Multiply twice since Angle AOD and BOD are equal due to similar triangles. After that you'll get Angle AOB.
The answer should be 2.37 (3 s.f) in radians. Use the calculator value for parts b), c) and d) for accuracy
B) In this question you just need to input the formula Area = ½ x r²(∅-sin∅). Ø is the answer from part A).
The answer should be 53.7 (3 s.f) Use calculator value for parts c) and d) for accuracy.
C) In this question you just use the formula of Surface Area x Height. Surface Area is your segment area and height is 25cm.
The answer should be 1342 (nearest whole) or 1340 (3 s.f). Use calculator value for part D) for accuracy.
D) In this part you will take the volume of water found in part (C) and divide that by the surface area of the cylinder (circle area). To find the S.A of the cylinder, π(r²) where r is the radius, 8cm. Afterwards, use the calculator value of C) and divide.
Your answer should be 6.67 (3 s.f)
Date Posted:
7 months ago
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