**IBDP** **Mathematics**** Question Analysis Topic: Mathematics - Volume and Surface Area**

**Exam Question:**

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)

**Answer:**

For IBDP Mathematics, you should know:

(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

Now:

Slant height **L** can thus be found by √[h^{2} + (r2 - r1)2]

= √[(24)^{2} + (15 - 5)2]

= √(576 + 100) = 26 cm

Next:

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 + πr1^{2}

= 1632.8 + 78.5 = 1711.3 cm^{2}

(ii) The bucket ought not to be made with ordinary plastic, as such material is **non-biodegradable** and **harmful to the environment**.

Work hard for your IBDP Mathematics examination!

End of analysis. Great!