A toy is in the shape of a cone mounted on a hemisphere of same base r

1.	A toy is in the shape of a cone mounted on a hemisphere of same base radius if the volume of the toyis 231cm ans its diameyer is 7cm find the height of the toy
Answer» Answer: 14.5003 cm Step-by-step EXPLANATION: Let the HEIGHT of cone be H Diameter of cone = 7 cm Radius of cone = $\frac{7}{2}=3.5 cm$ Volume of cone = $\frac{1}{3} \pi r^2 h$ = $\frac{1}{3} \times \frac{22}{7} \times 3.5^2 h$ = $12.833h$ Radius of HEMISPHERE = 3.5 cm Volume of hemisphere = $\frac{2}{3} \pi r^3$ = $\frac{2}{3} \times \frac{22}{7} \times 3.5^3$ = $89.833$ TOTAL volume of toy = 12.833h + 89.833 We are given that the volume of the toy is 231 cm . $12.833h + 89.833 = 231$ $12.833h = 231-89.833$ $12.833h = 141.167$ $h = \frac{141.167}{12.833}$ $h =11.0003$ Height of toy = 11.0003 + 3.5 = 14.5003 Hence the height of the toy is 14.5003 cm