Chapter U3, Problem 2STP

Interpretation Introduction

Interpretation:

The volume of rain for a height of 9 cm collected in a cylindrical gauge needs to be calculated given an initial volume of 6 ml collected for a height of 2 cm rain.

Concept introduction:

The volume 'V' occupied by a cylinder of height 'h' and radius 'r is given as:

${\text{V = πr}}^{\text{2}}\text{h -----(1)}$

Answer to Problem 2STP

(C) 27 ml

Explanation of Solution

Given:

Volume of rain for a height (h) of 2 cm is, V = 6 ml

Calculation:

Step 1: Calculate the radius 'r' of the cylinder

Based on equation (1):

$\begin{array}{l}{\text{V = πr}}^{\text{2}}\text{h }\\ \text{r = }\sqrt{\frac{\text{V}}{\text{πh}}}\\ \text{= }\sqrt{\frac{{\text{6 cm}}^3}{\text{3}\text{.142}\times 2\text{ cm}}}=0.977\text{ cm}\end{array}$

Step 2: Calculate the volume of rain of height 9 cm

Based on equation (1):

$\begin{array}{l}{\text{V = πr}}^{\text{2}}\text{h }\\ =3.142\times 0.977{\text{cm}}^{\text{2}}\times 9\text{ cm}\\ \text{=27}{\text{.0 cm}}^3\text{ or 27}\text{.0 ml}\end{array}$

Conclusion

Therefore, the volume of rain of height 9 cm collected in a cylindrical gauge is 27 mL.