Question

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Explanation:

Identify given values and formulas

We need to find the volume \(V\) and total surface area \(S\) of each solid. All measurements are in centimeters.

For a sphere of radius \(r\):

• Volume: \(V = \frac{4}{3}\pi r^3\)
• Surface Area: \(S = 4\pi r^2\)

For a hemisphere of radius \(r\) (including its flat circular base):

• Volume: \(V = \frac{2}{3}\pi r^3\)
• Total Surface Area: \(S = 3\pi r^2\) (curved surface \(2\pi r^2\) + base area \(\pi r^2\))

Solve Question 1

The first solid is a sphere. The radius is labeled as \(r = 9\text{ cm}\).

• Volume:

$$V = \frac{4}{3}\pi (9)^3 = \frac{4}{3}\pi (729) = 972\pi\text{ cm}^3 \approx 3053.63\text{ cm}^3$$

• Surface Area:

$$S = 4\pi (9)^2 = 4\pi (81) = 324\pi\text{ cm}^2 \approx 1017.88\text{ cm}^2$$

Solve Question 2

The second solid is a sphere. The diameter is labeled as \(1.8\text{ cm}\), so the radius is \(r = 0.9\text{ cm}\).

• Volume:

$$V = \frac{4}{3}\pi (0.9)^3 = \frac{4}{3}\pi (0.729) = 0.972\pi\text{ cm}^3 \approx 3.05\text{ cm}^3$$

• Surface Area:

$$S = 4\pi (0.9)^2 = 4\pi (0.81) = 3.24\pi\text{ cm}^2 \approx 10.18\text{ cm}^2$$

Solve Question 3

The third solid is a hemisphere. The radius is labeled as \(r = 12\text{ cm}\).

• Volume:

$$V = \frac{2}{3}\pi (12)^3 = \frac{2}{3}\pi (1728) = 1152\pi\text{ cm}^3 \approx 3619.11\text{ cm}^3$$

• Total Surface Area:

$$S = 3\pi (12)^2 = 3\pi (144) = 432\pi\text{ cm}^2 \approx 1357.17\text{ cm}^2$$

Answer:

Question 1

• Volume: \(972\pi\text{ cm}^3\) (or approximately \(3053.6\text{ cm}^3\))
• Surface Area: \(324\pi\text{ cm}^2\) (or approximately \(1017.9\text{ cm}^2\))

Question 2

• Volume: \(0.972\pi\text{ cm}^3\) (or approximately \(3.05\text{ cm}^3\))
• Surface Area: \(3.24\pi\text{ cm}^2\) (or approximately \(10.18\text{ cm}^2\))

Question 3

• Volume: \(1152\pi\text{ cm}^3\) (or approximately \(3619.1\text{ cm}^3\))
• Total Surface Area: \(432\pi\text{ cm}^2\) (or approximately \(1357.2\text{ cm}^2\))