I'm stuck with this math question please help me.?

Question

A cone is filled with ice-cream. It also has one scoop of ice cream on top in shape of a half sphere. The diameter of the sphere is 2 in and the height of the cone is 5 in. Calculate the volume of the ice-cream in cubic yards.

note: If you do know the answer can you please explain to me how you got it. Thank you.

how do I convert it to cubic yards?

can you please explain it you me in simple terms. I'm a noob in math thank you.

Answer 1

the volume of a sphere is given by
V(sph) = (4/3)*pi*r^3 where r is the radius,
while the volume of a cone is given by
V(cone) = (1/3)*pi*r^2*h where r is the radius and h is the height...

so finding the volume of the ice cream in the problem, we just take the half of the volume of the sphere and add it with the volume of the cone assuming the cone is completely filled with ice cream. here's the solution...

total Volume = V(cone) + V(sph) / 2
= (1/3)*pi*r^2*h + [ (4/3)*pi*r^3 ] / 2
= (1/3)*pi*2^2*5 + [ (4/3)*pi*2^3 ] / 2
= (1/3)*pi*4*5 + [ (4/3)*pi*8 ] / 2
= (1/3)*pi*20 + { [ (4/3)*pi*8 ] / 2 }

key-in all these in the calculator to get the exact value...i dont have the calculator at the moment :)

hey...i just found a calculator...the total volume is 37.70 cubic inches (rounded to two decimal places)

Answer 2

Draw the cone and half scope on top. You need to know the formula for a cone (V=(1/3)(pi)r^2h, and a sphere (V=I(4/3)(pi)r^3.. Now put the dimensions of the radii of cone and sphere (equal) and height of cone on yur diagram. It looks like you must add the volume of the cone to 1/2 the volume of a sphere (half a scoope). Remember your dimensions are all in inches so later we can change to cubic yards.

V(ice cream) =(1/3)(3.14)(1^2)5 + (1/2)(4/3)(3.14)1^3
=(5/3)(3.14) + (2/3)(3.14)
=(7/3)(pi) = 7.33 cubic inches

Now since there are 36 inches in a yard we have to divide each dimension used (or number of times use) by 36 to change each dimension to yards and end up with cubic yards.

V = (7/3)pi/(36x36x36) = 0.00005pi cubic yards or

= o.ooo157 cubic yards ice cream

Answer 3

Volume of cone = pir^2h/3 = 3.14*1^2*5/3=5.2333 in^3
Volume of hemispere is 2pir^3/3 = 2*1^3*3.14/3 = 2.093 in^3
Total volume = 5.233+2.0933 =7.33 in^3
1 cubic yard = 46,656 cubic inches
Thus answer is 7.33/46656 = 0.000157 cubic yards.

Answer 4

volume of cone = 1/3 (pi)r^2h
=1/3*22/7*1*1*5
=110/21
=5.23inches

Answer 5

I will not tell you the answer, but I will tell you how to get it.

If it is a half sphere, then find the volume as if it were a whole sphere and then divide by 2.

Answer 6

percents relate to their section from one hundred, so 40-one% potential 40-one/one hundred. Now you're asked to locate how plenty 40-one to one hundred is as 'X' to fifty six: 40-one/one hundred = X/fifty six the equation is solved: X = (40-one/one hundred) * fifty six = 22.ninety six to examine if it somewhat is genuine, you could locate if 40-one/one hundred is comparable to 22.ninety six/fifty six .