An ice cream cone has a diameter of 7 cm and its height is 9 cm. It is filled with a scoop of spherical shaped ice cream of radius 3.5 cm.

Given,

Height of cone(h) = 9 cm

Diameter of cone = 7 cm

Radius of cone (R) = $\frac{7}{2}$ = 3.5 cm

Radius of spherical scoop (r) = 3.5 cm

By formula,

$V_{cone} = \frac{1}{3}\pi r^2h$

Substituting values we get :

$$\begin{aligned}V_{cone} = \frac{1}{3} \times \frac{22}{7} \times (3.5)^2 \times (9) \\[1em] = \frac{22}{7} \times 12.25 \times 3 \\[1em] = \frac{22}{7} \times 36.75 \\[1em] = \frac{808.5}{7} \\[1em] = 115.5 \approx 116 \text{ cm}^3.\end{aligned}$$

By formula,

Volume of sphere = $\frac{4}{3} \pi r^3$

$$\begin{aligned}V_{\text{spherical scoop}}= \frac{4}{3} \times \frac{22}{7} \times (3.5)^3 \\[1em] = \frac{4}{3} \times \frac{22}{7} \times 42.875 \\[1em] = \frac{3773}{21} \\[1em] = 179.67 \approx 180 \text{ cm}^3.\end{aligned}$$

Since, 180 > 116,

Hence, the ice cream is in excess.

(b) Excess ice cream = Volume of spherical scoop - Volume of cone

= 180 – 116 = 64 cm³.

Hence, excess volume of ice cream = 64 cm³.