A solid cone is joined to a solid hemisphere to make the solid $\mathbf{T}$, as shown. The diameter of the base of the cone is $9 \mathrm{~cm}$. The diameter of the hemisphere is $9 \mathrm{~cm}$. The total volume of $\mathrm{T}$ is $140 \pi \mathrm{cm}^{3}$ The total height of $\mathrm{T}$ is $y \mathrm{~cm}$. a) Calculate the value of $y$. Give your answer correct to 3 significant figures. Vol of sphere $=\frac{4}{3} \pi r^{3}$ Optional working The diameter of the base of the cone and the diameter of the hemisphere are both increased by the same amount. b) Assuming the total volume of $T$ does not change, select which statement below applies. A - your answer to part (a) would increase. B - your answer to part (a) would decrease. C - your answer to part (a) would not change. (1) Answer $\mathrm{cm}$ (4) Total marks: 5

Step 1 ：First, let's find the radius of the hemisphere and the base of the cone by dividing the diameter by 2: \(r = \frac{9}{2} = 4.5\) cm.

Step 2 ：Next, let's find the volume of the hemisphere using the formula \(V_{hemisphere} = \frac{2}{3} \pi r^3\): \(V_{hemisphere} = \frac{2}{3} \pi (4.5)^3 = 60.75\pi\) cm³.

Step 3 ：Let's find the volume of the cone using the formula \(V_{cone} = \frac{1}{3} \pi r^2 h\), where h is the height of the cone.

Step 4 ：Since the total volume of the solid T is the sum of the volumes of the hemisphere and the cone, we can set up an equation to solve for y, the total height of the solid T: \(\frac{2}{3} \pi r^3 + \frac{1}{3} \pi r^2 h = 140\pi\).

Step 5 ：Plug in the values we know: \(60.75\pi + \frac{1}{3} \pi (4.5)^2 h = 140\pi\).

Step 6 ：Solve for h: \(h \approx 11.741\) cm.

Step 7 ：Finally, add the height of the cone to the radius of the hemisphere to find the total height of the solid T: \(y = h + r \approx 11.741 + 4.5 = 16.241\) cm.

Step 8 ：\(\boxed{y \approx 16.241}\) cm (correct to 3 significant figures).