Question

1. calculate the surface area

Explanation:

Step1: Find the radius of the hemisphere and cone

The diameter of the hemisphere and the base - diameter of the cone is 18 cm, so the radius $r = \frac{18}{2}=9$ cm.

Step2: Calculate the slant - height of the cone

The slant - height $l$ of the cone can be found using the Pythagorean theorem. Given the height of the cone is not needed here as we know the slant - height $l = 15$ cm.

Step3: Calculate the surface area of the hemisphere

The surface area of a hemisphere $A_{hemisphere}=2\pi r^{2}$. Substituting $r = 9$ cm, we get $A_{hemisphere}=2\pi\times9^{2}=2\pi\times81 = 162\pi$ $cm^{2}$.

Step4: Calculate the lateral surface area of the cone

The lateral surface area of a cone $A_{cone}=\pi rl$. Substituting $r = 9$ cm and $l = 15$ cm, we get $A_{cone}=\pi\times9\times15 = 135\pi$ $cm^{2}$.

Step5: Calculate the total surface area

The total surface area $A = A_{hemisphere}+A_{cone}$. So $A=(162\pi + 135\pi)=297\pi$ $cm^{2}$. Taking $\pi\approx3.14$, $A = 297\times3.14=932.58$ $cm^{2}$.

Answer:

$932.58$ $cm^{2}$