Question

. A sphere is inscribed in a cube. Find the lateral area of the cube if the area of the sphere is 784π.

Answer 1

Did you know the formula for the area of the sphere ?

Answer 2

4 pi r squared

Answer 3

Can u find the radius r, from te give question?

Answer 4

do you know what is the lateral surface area of cube

Answer 5

4b^2=lateral surface area of cube

Answer 6

the radius is 4.998732447

Answer 7

like r=4.9

Answer 8

right i think so.

Answer 9

dis gon b gud

Answer 10

wat do u think is the answer? pls help me that`s our take home finals
tnx.

Answer 11

\[A_{sphere}=4{\pi}r^{2}\]\[784\pi=4{\pi}r^{2}\]\[r^{2}=\frac{ 784 }{ 4 }\]\[r=14\]Since r is half of the side of the cube, the length of the side of the cube (b) is equal to 2r .
Thus \[A_{l}=5b^{2}=5(2r)^{2}=5(2\times14)^{2}=3920\]

Answer 12

so that is the lateral area of the cube?

Answer 13

yep

Answer 14

@mayankdevnani can you confirm?

Answer 15

thank you, do you think you can help me with the other one? if not its ok

Answer 16

what? @Algebraic!

Answer 17

. Suppose the lateral area of a right circular cone and the area of a sphere equal 64π in2. If the radius of the sphere and the radius of the base of the cone are equal, what is the volume of the cone? (10 points)

Answer 18

@Zekarias plz tell me what is lateral surface area of cube

Answer 19

L.S.A of a cube = 4l^2

Answer 20

@Zekarias not 5l^2

Answer 21

yaa that's what i called this question

Answer 22

LSA of a regular object is Perimeter of base times height.

Answer 23

sorry you are right. It 4b^{2}

Answer 24

so what is the L S A of the cube?

Answer 25

sauravshakya so how is the solution??

Answer 26

\[4(2r)^{2}\]

Answer 27

@Zekarias would like to do that.

Answer 28

4(2r^2)=4(2*14^2)=1568

Answer 29

ok @dylan18

Answer 30

ok @Zekarias @ sauravshakya

Answer 31

@mayankdevnani that is the soulution?

Answer 32

NOPE @mayankdevnani

Answer 33

yaa

Answer 34

LSA of a cube =4 l^2 = 4*(2*14)^2 = 3136

Answer 35

@Zekarias i think he can do that

Answer 36

square units

Answer 37

i mean you @Zekarias

Answer 38

yaa sry

Answer 39

thnx.. @sauravshakya

Answer 40

ah... the unit is square units.. is that the answer?

Answer 41

yaa

Answer 42

ahhh., thank you very much

Answer 43

thank you very much @Zekarias ,@sauravshakya ,@mayankdevnani you think you can help me last one.?

Answer 44

welcome

Answer 45

6. Suppose the lateral area of a right circular cone and the area of a sphere equal 64π in2. If the radius of the sphere and the radius of the base of the cone are equal, what is the volume of the cone? (10 points) tnx

Answer 46

you think that is enough @Zekarias ?

Answer 47

What is the question now?

Answer 48

6. Suppose the lateral area of a right circular cone and the area of a sphere equal 64π in2. If the radius of the sphere and the radius of the base of the cone are equal, what is the volume of the cone? (10 points)

Answer 49

Ok to find the volume of a cone you need to have the height (h) and radius of the base (r).
To do that u need to find the slant height (l).
Did u know the formula for the lateral surface area of a cone?

Answer 50

i think the LSA is in the question.

Answer 51

It the voume what u asked
Any how .....here is what I asked u befor\[A_{l..cone}={\pi}rl...and .....A_{sphere}=4{\pi}r^{2}\]

Answer 52

\[A_{l..cone}={\pi}rl=A_{sphere}=4{\pi}r^{2}\]since bothe are equal

Answer 53

π × r × l, like this?

Answer 54

yes

Answer 55

then how should we used that?

Answer 56

Now our goal is to find l first. ok

Answer 57

yes.. i think we can used base*height?

Answer 58

\[A_{sphere}=4{\pi}r^{2}=64\pi\]\[r^{2}=16\]\[r=4\]and \[A_{l..cone}={\pi}rl=64\pi......but ..r=4\]\[4l=64\]\[l=16\]

Answer 59

Now can u find h

Answer 60

SO NOW WE can substitute to find the height

Answer 61

yes

Answer 62

U get this \[h=4\sqrt{15}\]

Answer 63

15.49

Answer 64

Now the volume of the cone is given by\[V=\frac{ 1 }{ 3 }{\pi}r^{2}h\]

Answer 65

can u finish it?

Answer 66

(1/3) * pi * r2 * h

- or -

3.14159 *r2 * l * 4/3

Answer 67

correct
i out now
GOOD BY

Answer 68

thanks