10 A frustum is a portion of a solid. The frustum shown opposite is formed from a cone. a What is the volume of the missing top cone? Give answers correct to the nearest cubic metre.
b What was the volume of the entire cone?
c What is the volume of the frustum?

Step-by-step explanation:

all you needed to do was a quick search on the internet : "volume of a cone".

and you get immediately :

pi×r²×h/3

the reason is similar to all other volume formulas : base area times height. for pyramids and cones there are factors included to reduce this a bit, because they simply don't go straight up from their base area, so they have less volume than comparable objects that do go straight up (like a cylinder compared to a cone).

r = radius

h = height

so, for a) we only need to use the calculator :

pi × 5² × 30 / 3 = pi×25×10 = 785.4 ≈ 785 m³

for b) we need to do the same thing, but with r = 10 and h = 60.

pi × 10² × 60 / 3 = pi×100×20 = 6283.2 ≈ 6283 m³

so, for c) we only need to subtract the result of a) from the result of b)

the frustum is the volume of the large cone minus the volume of small, top cone.

6283 - 785 = 5498 m³