Geometry of Packaging?

Question

1)The diameter of a soft ball is about 10.2 cm, what is its volume?

2)What is the volume of a pyramid shaped box that is 20cm tall and has a regular hexagonal base with side lengths of 15cm

Funny, i dont remember asking for your opinions in the question.

Answer 1

Seriously, do your own homework. Who are you testing when you can just go look up the formula for volume of a sphere etc?

This is utmost laziness.

Answer 2

Answers with Solutions

Qns. 1:

Diameter = 10.2 cm
Radius = 5.1 cm
Volume of a sphere = 4/3 * π * r^3
= 4/3 * π * 5.1^3
= 555.65 cm sq.
≈ 556 cm sq. (nearest cm sq.)

Qns. 2:

Vol. of pyramid = 1/3 * Base Area * Ht.
Ht. of pyramid = 20 cm

Regular hexagon (6-sided):
Exterior Angle = 360 / 6
= 60 deg.
Interior Angle = 180 - 60
= 120 deg.

Hexagon gives us 4 equal triangles.
Base Area = 4 ( 0.5 * 15 * 15 * sin 120 )
≈ 389.71 cm sq.

Therefore,
Vol. of pyramid = 1/3 * 389.71 * 20
= 2 598.08
≈ 2598.1 cm sq.

Hope This Solutions Will Help In Answering Your Questions ;)

G0n9 G0n9™
Mathematician

Answer 3

Volume of a sphere of radius r is 4/3 pi r^3

Since diameter of the ball is 10.2 cms, its radius will be half of it, i.e. 5.1 cms.

So, V = 4/3 x 3.1416 x 5.1 x 5.1 x 5.1 = 555.65 cc

Coming to your second question:

V = 1/2 sqrt3 h.a^2 where h is the height of the pyramid and a is the length of one side.

V = 1/2 x sqrt3 x 20 x 15 x 15 = 3897.11 cc

Answer 4

1) Sphere Volume = 4/3 • π • r³ = ( π •d³)/6
555.37

2)The volume of a cone is 1/3(Area of Base)(height) = 1/3 π r2 h

Answer 5

1.) (10.2/2)^3*4/3pi =
5.1^3*4.19 =
132.651*4.19 =
555 cm^3

Answer 6

I agree with Tall Paul and would urge all users to refrain from helping students in their homework... I mean this is just spoon-feeding.

Answer 7

You might not like our opinions but you got em. Figure it out lazy. and one more thing

OH MY GOD!!!!!!!!!!!!
OH MY GOD!!!!!!!!!!!!
OH MY GOD!!!!!!!!!!!!
Remember that one...dork.