For making a toy, a hemisphere is attached at one end of a cylinder and a cone is attached at the other end of the cylinder. The cylinder, the cone and the hemisphere have a common radius of 4.2 cm. The height of the cylinder and that of the cone is 7 cm. Find the volume (in cm$$^3$$​) of the toy. (Use $$\pi$$ = $$\frac{22}{7}$$​)

Correct option is C

Given:
Common radius (r) of hemisphere, cylinder, and cone = 4.2 cm.
Height of the cylinder ($$h_{\text{cylinder}}$$​) = 7 cm.
Height of the cone ($$h_{\text{cone}}$$​) = 7 cm.
​$$π = \frac{22}{7}$$​​
Formula Used:
Volume of a Hemisphere:
$$V_{\text{hemisphere}} = \frac{2}{3} \pi r^3$$​
Volume of a Cylinder:
$$V_{\text{cylinder}} = \pi r^2 h$$​
Volume of a Cone:
​$$V_{\text{cone}} = \frac{1}{3} \pi r^2 h$$​
Solution:
$$V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 = \frac{2}{3} \times \frac{22}{7} \times (4.2)^3$$​​

​$$V_{\text{hemisphere}} = \frac{2}{3} \times \frac{22}{7} \times 74.088$$​

​$$V_{\text{hemisphere}} = \frac{2}{3} \times 22 \times 10.584 = \frac{2}{3} \times 232.848 = 155.232 \text{ cm}^3$$​

​$$V_{\text{cylinder}} = \pi r^2 h = \frac{22}{7} \times (4.2)^2 \times 7$$​

​$$V_{\text{cylinder}} = \frac{22}{7} \times 17.64 \times 7 = 22 \times 17.64 = 388.08 \text{ cm}^3$$​

​$$V_{\text{cone}} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times (4.2)^2 \times 7$$​​

​$$V_{\text{cone}} = \frac{1}{3} \times \frac{22}{7} \times 17.64 \times 7 = \frac{1}{3} \times 22 \times 17.64 = \frac{388.08}{3} = 129.36 \text{ cm}^3$$​

​$$V_{\text{total}} = V_{\text{hemisphere}} + V_{\text{cylinder}} + V_{\text{cone}}$$​= 155.232 + 388.08 + 129.36
​$$V_{\text{total}} = 672.672 \text{ cm}^3$$​