a sphere or radius 4cm is melted down to form a cone of the same radius. what height is this cone?

Question

*sphere of radius*

please explain fully

thanks

Answer 1

Write down the 2 formulas:

Volume of a sphere:
V = (4/3)*pi*r^3

Volume of cone:
V = 1/3 * Pi * r^2 * h
They are equal, so simplify from there. only h is unknown.
I would multiply both sides by 3 first to eliminate the thirds:

4 pi r^3 = pi r^2 h

divide both sides by pi, and by r^2

4 r = h
we know r = 4cm

16cm = h

Answer 2

If the sphere is "melted down" and made into a new shape, I guess the implication is that the volume would be the same because the amount of material hasn't changed. Use r = 4cm and the formula for the volume of a sphere (V =(4/3)pi*r^3) to find the volume. Then that this volume and the radius and use them in the forumla for a cone's volume (V=(1/3)pi(r^2)h ) to solve for the hieght, "h". Or even better, set the two volumes equal to each other, let some terms cancel out, plug in r, and solve for h.

Answer 3

Well, no hint required, actually because the question itself is very easy. ______________________________________... As per question - Vol. of sphere = Vol of cone (lets take radius of sphere as r and radius and height of cone as r' and h, respectively) 4/3 x (pi) x r ^3 = 1/3 x (pi) x r' ^2 x h 4/3 x r ^3 = 1/3 x 4 x 4 x16 (after cancelling the pies and subt. the given values) 4/3 x 3 x 1/4 x 1/4 x r ^3 =16 (after taking 1/3 and 4s to the L.H.S. 4 and 3 can get cancelled) 1/1 x 1 x 1/1 x 1/4 x r ^3 =16 Therefore, r ^3 =16 x 4 ie, r^3 = 4 x 4 x 4 Thus r = 4 (Answer)

Answer 4

it is a volume problem

volume of a sphere = (4/3)*pi*r^3
volume of a cone = V = hB/3 (where B is the area of the base) or
V = h*pi*r^2/3

set the volumes equal to eachother

4/3*pi*r^3=h*pi*r^2/3

cancel like terms

4r=h

h=16cm

Answer 5

volume of sphere=4/3*3.14*r^3
=4/3*3.14*4^3
=4/3*3.14*64
=267.95cm^3
now
volume of sphere=1/3*3.14*r^2*h = 267.95
=1/3*3.14*4^2*h= 267.95
16.74h=267.95
h=267.95/16.74
h=16.00657 cm
ANSWER

Answer 6

Find the voloume of both and equate them you will get your answer