Can someone please help with q22, 23 and 24 (1 Viewer)

kpad5991 · Jan 23, 2018

fan96 · Jan 23, 2018

22)

Find the area of the sector $OAB$ and subtract it from the area of the triangle $OAB$ .
_________________________________________________________________________________________

23)

a) The arc $AB$ is equal to the circumference of the cone's base. With that information you can calculate the radius.

b) Once you know the slanted height of the cone and its base's radius, you can form a triangle to calculate the perpendicular height.

c) Use the volume formula for a cone.

d) The curved surface area is equal to the area of the sector $OAB$ .
_________________________________________________________________________________________

24)

a) First calculate the area of the sector $OPQ$ in terms of $r$ and $\theta$ . Then express $r$ in terms of $\theta$ by using the perimeter and the arc length formula.

b) Differentiate the area formula and identify its maximum value. The domain should be $0 < \theta < \pi$ , but it might not matter either way.

kpad5991 · Jan 23, 2018

How is the solution 4/3 (4pi -3 root 3) i got 4/3(2 Pi - 3 root 3)

fan96 · Jan 23, 2018

kpad5991 said:
How is the solution 4/3 (4pi -3 root 3) i got 4/3(2 Pi - 3 root 3)

Gonna need a bit more information.... what question?

kpad5991 · Jan 23, 2018

fan96 said:
Gonna need a bit more information.... what question?

Sorry q22

integral95 · Jan 23, 2018

fan96 said:
22)

Find the area of the sector $OAB$ and subtract it from the area of the triangle $OAB$ .
_________________________________________________________________________________________

23)

a) The arc $AB$ is equal to the circumference of the cone's base. With that information you can calculate the radius.

b) Once you know the slanted height of the cone and its base's radius, you can form a triangle to calculate the perpendicular height.

c) Use the volume formula for a cone.

d) The curved surface area is equal to the area of the sector $OAB$ .
_________________________________________________________________________________________

24)

a) First calculate the area of the sector $OPQ$ in terms of $r$ and $\theta$ . Then express $r$ in terms of $\theta$ by using the perimeter and the arc length formula.

b) Differentiate the area formula and identify its maximum value. The domain should be $0 < \theta < \pi$ , but it might not matter either way.

Q22

OA = OB = 4cm

fan96 · Jan 23, 2018

I just realised I made a mistake with that diagram. The radius should be 4cm, not 2cm.

$\angle OAB = 2 \cos^{-1}(0.5) = \frac{2\pi}{3}$

Area of sector $OAB$

$= \frac{1}{2} (4)^2 \left(\frac{2\pi}{3}\right)$

$= \frac{16\pi}{3}$

Area of triangle $OAB$

$= \frac{1}{2} (4) (4) \sin \frac{2\pi}{3}$

$= 4\sqrt 3$

Area of shaded segment

$= \frac{16\pi}{3} - 4\sqrt 3$

$= \frac{4}{3}\left(4\pi - 3\sqrt 3\right)$

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Can someone please help with q22, 23 and 24 (1 Viewer)

kpad5991

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fan96

617 pages

kpad5991

Member

fan96

617 pages

kpad5991

Member

integral95

Well-Known Member

fan96

617 pages

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