(a) 150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, and are completely…

Let \(\displaystyle h \mathrm{~cm}\) be the rise in the water level. Then \[\begin{aligned} & \pi(3 \cdot 5)^{2} h=\frac{4 \pi}{3}(0 \cdot 7)^{3}(150) \\ & \Rightarrow h=5 \cdot 6 \mathrm{~cm} \\ & \text { (b) } \quad \begin{array}{l} \text { Three cubes of side } 6 \mathrm{~cm} \text { each, are joined as shown in Figure } 1 . \\ \text { Find the total surface area of the resulting cuboid. } \end{array} \end{aligned} \] Length of cuboid=18cm Total surface area of solid \(\displaystyle =2(18 \times 6+6 \times 6+6 \times 18)\) \[=504 \mathrm{~cm}^{2} \]