Question

. Spherical Wedge. A portion of spherical cheese (queso de bola) was sliced in the form of a spherical wedge. The diameter of the cheese (wax included) is 3 inches. Calculate the volume of the wedge if the angle is 45o. Calculate the outer surface area of the wax taken-off.

Answer 1

Yes. The one i did was the total surface area

Answer 2

Help please @paki

Answer 3

@One098 @KamiBug help

Answer 4

@ganeshie8

Answer 5

@iambatman

Answer 6

we can use this
http://en.wikipedia.org/wiki/Spherical_wedge

Answer 7

The volume i got is 101.25 @perl

Answer 8

one moment

Answer 9

definition spherical wedge
(geometry) A volume of a sphere lying between two vertical planes through the centre of the sphere.

Answer 10

in radians there is a nice formula for volume

V = 2/3 * a * r^2 , where 'a' is the center angle in radians

Answer 11

45 degrees = pi/4 radians
V = 2/3 * pi/4 * (3/2)^2 ,

Answer 12

inches cubed

Answer 13

Its (3/2)^3

Answer 14

the diameter was given as 3 inches, so r = 3/2

Answer 15

oh sorry

Answer 16

V = 2/3 * pi/4 * (3/2)^3 *

Answer 17

V = 9/16 * Pi

Answer 18

you may simply scale the volume for the given angle : \[V = \dfrac{\pi/4}{2\pi}\left( \dfrac{4}{3}\pi r^3 \right) = \frac{1}{8}\left( \dfrac{4}{3}\pi \left(\frac{3}{2}\right)^3 \right) = \frac{9\pi}{16}\]

Answer 19

right thats basically what you are doing
volume of wedge = theta/ 2pi * ( volume of sphere)

Answer 20

you can do the same thing for surface area also
just keep in mind you got two more faces when you chop off a slice

Answer 21

and similarly for surface area

Surface area of wedge = theta/ 2pi * (surface area of sphere)

Answer 22

How about the area ?

Answer 23

3pi/4 b

Answer 24

similarly for outer surface area of wedge

Outer Surface area of wedge = theta/ 2pi * (surface area of sphere)

area = (pi/4) / (2pi ) * 4 * pi * r^2

Answer 25

?*

Answer 26

Area = (pi/4) / (2pi ) * 4 * pi * (3/2)^2
= 1/2 * pi * 9/4
= 9/8 pi inches ^2

Answer 27

because surface area of sphere is 4*pi*r^2

Answer 28

I got comfused on the (pi/4)/(2pi)

Answer 29

Is it really 9/4