IBDP Mathematics Question Analysis Topic: Mathematics - Volume and Surface Area
The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find
(i) The area of the metal sheet used to make the bucket ?
(ii) Why we should avoid the bucket made by ordinary plastic (Use π = 3.14)
(i) First, let's sort out the given information:
Height of frustrum h = 24 cm
Radius of bucket's lower end r1 = 10/2 = 5 cm
Radius of bucket's upper end r2 = 30/2 = 15 cm
Slant height L can thus be found by √[h2 + (r2 - r1)2]
= √[(24)2 + (15 - 5)2]
= √(576 + 100) = 26 cm
The area of the metal sheet used to construct the bucket is equal to the total surface area of the bucket (with the exception of the upper end)
So, the total surface area = π(r1 + r2)L + πr12
= 1632.8 + 78.5 = 1711.3 cm2
(ii) The bucket ought not to be made with ordinary plastic, as such material is non-biodegradable and harmful to the environment.
End of analysis. Great!