Question

If the radii of the circular ends of a bucket of height 40cm are 35 cm and 14 cm, respectively, then the volume of the bucket in cubic centimetre is ( approx. in cubic cm).
(a) 60060
(b) 80080
(c) 70070
(d) 80160

Answer 1

Hint: The first thing you should know is that the shape of the bucket is a frustum. So, we are given the height and the radius of the ends of the frustum and we are asked the volume of it. We know that the area of the frustum is given by $\dfrac{1}{3}\times \pi \times h\times \left( {{r}_{1}}^{2}+{{r}_{2}}^{2}+{{r}_{1}}{{r}_{2}} \right)$ , So, just put the values and solve to get the answer.

Complete step-by-step answer:
Let us start the solution to the above question by drawing a diagram of the situation given in the question. We know that a bucket generally has the shape of a frustum.

Now, we know that the area of the frustum is given by $\dfrac{1}{3}\times \pi \times h\times \left( {{r}_{1}}^{2}+{{r}_{2}}^{2}+{{r}_{1}}{{r}_{2}} \right)$ . It is also given in the question that the radii are 35cm and 14cm, while the height is 40cm. If we put this in the formula, we get
 $\text{Volume of bucket}=\dfrac{1}{3}\times \pi \times h\times \left( {{r}_{1}}^{2}+{{r}_{2}}^{2}+{{r}_{1}}{{r}_{2}} \right)$
$\Rightarrow \text{Volume of bucket}=\dfrac{1}{3}\times \pi \times 40\times \left( {{35}^{2}}+{{14}^{2}}+35\times 14 \right)$
$\Rightarrow \text{Volume of bucket}=\dfrac{1}{3}\times \pi \times 40\times \left( 1225+196+490 \right)$
Now, if we put $\pi =\dfrac{22}{7}$ , we get
$\Rightarrow \text{Volume of bucket}=\dfrac{1}{3}\times \dfrac{22}{7}\times 40\times 1911=80080c{{m}^{3}}$
The option closest to our answer is option (b), i.e., 80080.
Hence, the answer is option (b).


Note: It is important that you remember the formulas related to the volume of the frustum and other three dimensional figures as they are used very often. Whenever you are asked to report the approximate answer, report the closest option as we did in the above question. Be careful about the calculation part as well, as the only place to make an error in the above question is in the calculation part.