GCSE Mathematics Question Analysis Topic: Mathematics - Volume
Exam Question:
A heap of rice is in the form of a cone of base diameter 24, and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?
Answer:
For GCSE Mathematics, you should know:
We are given that the heap of rice is cone-shaped i.e.,
Diameter d = 24m
Radius r = d/2 = 12m
Height h = 3.5m
Volume of cone V = πr2h/3
V = (π x 122 x 3.5) / 3 = 528 m3
Now, we're told that the canvas cloth is required to cover the (cone-shaped) heap. In other words, it needs to cover the exact curved surface area of the cone.
Slant height of cone l = √(h2 + r2)
= √(3.52 + 122) m
= 12.5 m
Curved surface area of the 'cone' S = πrl
S = 22/7 x 12 x 12.5 m2
S = 471.42 m2
The following diagram is for your reference:
Work hard for your GCSE Mathematics examination!
End of analysis. Great!