Help with these problems please?

Question

I need to find the surface area and volume for each of these figures...

A cylinder with a diameter of 18m and with the height of 12m. On top of the cylinder is a cone that is also 12m high. I know the surface area of this one (1161m^2), but I'm having issues with the volume.

The next figure is a rectangular prism, with the depth (?) of 16cm and it is 30cm high. On top of it is a half-cylinder, with a given height of 10. I really struggled with this one... can anyone help?

Answer 1

First one:

Vcyl = pi * r^2 * h | d = 18, h = 12m, r = d/2
Vcone = (pi * r^2 * h)/3 | Scone = pi * r * (r + s) | Scone = 1161, h = 12m, h^2 + r^2 = s^2 >> s = sqrt(h^2+r^2)

1161 = pi * r * (r + sqrt(12^2 + r^2)) ... r = 12.44
Vcone = (pi * 12.44^2 * 12)/3 = 1944.69
Vcyl = pi * 9^2 * 12 = 3053.63

Vcone + Vcyl = 4998.32 ~ 5000m³

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Second one:

Assuming that the half-cylinder has the same measures as the prism, the height of the half cylinder (10cm, which then acutally is its radius) is half of the width of the prism:

Vhcyl = (pi * 10^2 * 10)/2 = 1570.8
Vprism = 20*16*30 = 9600

Answer 2

Well in the second problem u havent mentioned the dia of cylinder n the unit for its height is missing

Answer 3

Volume formula for a cylinder

v = π r² h

v = 3.141592654(9)²(12)

v = 3.141592654(81)(12)

v = 254.4690049(12)

v = 3053.628059 m

V = 3053.6 m rounded to one decimal place

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