Help me in maths.?

Question

A right triangle with sides 3cm and 4am is revolved around its hypotenuse. Find the volume of the double cone thus generated.

Answer 1

Hi, Eka g.

Can you follow me like this?

1.The base of this right triangle is 3 or 4, and the proportion of the right triangle is 3 : 4 : 5 (When the base is 3, the height is 4, and the hypo is 5).
(When the base is 4, the height is 3, and the hypo is 5.)

2. The area of each circle are 3 X 3 x π and 4 x 4 x π

3. The volume of the double cone are

3 x 3 x π x 4 x 1/3 = 9 x 4/3 x π　= 36/3 π = 12π　
4 x 4 x π x 3 x 1/3 = 16 x 3/3 x π = 48/3 π = 16π


The answers are 12 π and 16 π

*key points of this Q are as follows:

1.The hypotenuse and proportion of the right triangle 3:4:5.
2.The base r and the height h.
3.The area of a circle is pi times the radius squared: πr"2"
4.The volume of the cone: πr"2" x h x 1/3

You can continue now. :-) Good luck!

Cheers!

Answer 2

The rotation produces 2 cones that share the same base.

The volume of a cone is 1/3 the area of the base times the height and the area of the base is pi * r^2. We need first to find the radius, r, of the base and the height of each cone for our calculation.

You already know from the Pythagorean theorem that the hypotenuse is 5 cm [sqrt (3^2 + 4^2)].

Label the hypotenuse AB and the third corner of the triangle C. A line perpendicular to the hypotenuse from point C is the radius of the base shared by the 2 cones. If the height of one of the cones is h, the height of the other cone is 5 - h.

Apply the Pythagorean theorem to the 2 new triangles:

r^2 + h^2 = 3^2
r^2 + (5-h)^2 = 4^2

Solve each equation for r^2:

r^2 = 9 - h^2
r^2 = 16 - (5 - h)^2

Set the two expressions for r^2 equal to each other:

16 - (5 - h)^2 = 9 - h^2
16 - (25 -10h + h^2) = 9 - h^2
16 - 25 + 10h - h^2 = 9 - h^2
-9 + 10h = 9
10h = 18
h = 18/10 = 1.8

Plug this result into our first equation

r^2 + (1.8)^2 = 9
r^2 +3.24 = 9
r^2 = 9 - 3.24
r^2 = 5.76

We can stop here because we only need to know r^2.

Volume of cone = pi*r^2*h/3

Volume of first cone = pi(5.76)(1.8)/3
Volume of second cone = pi(5.76)(5 - 1.8)/3

Answer 3

The 3,4,5 triangle when revolved around it's hypotenuse generates a double cone. Part of the hypotenuse serves as a radius for the first cone and the remaining part for the second one.
let r= radius of 1st cone
R= radius of 2nd cone
Volume of a cone = (1/3) (pi*r^2)h
Both cones share the same height(the altitude of the triangle which can be calculated by using similar triangles. But this one is an easier way of finding the altitude,
Area of a triangle = .5*4*3 = 6
Area of a triangle = .5*altitude*hypotenuse = .5*alt*5=6
altitude=2.4 cm (this is the height for both cones)

To find the radius of both cones, use Pythagorean theorem
The altitude divides the triangle into two smaller triangle.
1st triangle has height = 2.4, hyp = 3 and unknown base.
3^2 -2.4^2 = base^2 =3.24 (leave the base to the second power cos it is helpful that way)
therefore,radius of cone 1 : r =sqrt3.24

similarly,
2nd triangle has height = 2.4, hyp = 4 and unknown base.
4^2 -2.4^2 = base^2 =10.24 (leave the base to the second power cos it is helpful that way)
therefore,radius of cone 2: R =sqrt10.24
Volume = Volume of Cone 1 +Volume of Cone 2
= (1/3) (pi*r^2)h +(1/3) (pi*R^2)h
=(pih/3)(r^2 + R^2)
=(pi0.8)(3.24+10.24)
=10.784pi cm^3

Answer 4

just follow me u'll get the answer
the hyp is 5cm
r=2.5cm
l1=3cm
l2=4cm
h1=sqrt(l1*l1 - r*r)
h2=sqrt(l2*l2 - r*r)
volume of the double cone is (1/3)pi*r*r(h1+h2)
find it out
all the best

Answer 5

Come dude u can do this ur self with a help of a calulator

Answer 6

I can't help with math but wanted to mention you could also use some help with spelling. Good luck!

Answer 7

consult a westermans guide

Answer 8

im not sure but you can go on math.com for some help

Answer 9

http://mathworld.wolfram.com/

Answer 10

what is 4AM? do you mean 4cm?