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Identify the given diameter.

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4 parts
a

7 cm\text{7 cm}

b

615.75 cm2\text{615.75 cm}^2

c

1436.76 cm3\text{1436.76 cm}^3

d

461.81 cm2\text{461.81 cm}^2

Step-by-step solution

11 steps

Here's the solution for Question 9:

Part a· 2 steps

  1. Identify the given diameter.

    The diameter of the sphere is 14 cm.

  2. Calculate the radius.

    The radius (rr) is half of the diameter.

    r=diameter2r = \frac{\text{diameter}}{2} r=14 cm2r = \frac{14 \text{ cm}}{2} r=7 cmr = 7 \text{ cm}

    The radius of the sphere is 7 cm\boxed{\text{7 cm}}.

Part b

615.75 cm2\text{615.75 cm}^2

  1. Identify the radius.

    The radius is r=7r = 7 cm.

  2. Substitute the radius into the surface area formula for a sphere.

    SA=4πr2\text{SA} = 4\pi r^2 SA=4×π×(7 cm)2\text{SA} = 4 \times \pi \times (7 \text{ cm})^2 SA=4×π×49 cm2\text{SA} = 4 \times \pi \times 49 \text{ cm}^2 SA=196π cm2\text{SA} = 196\pi \text{ cm}^2 SA≈196×3.14159265... cm2\text{SA} \approx 196 \times 3.14159265... \text{ cm}^2 SA≈615.75216 cm2\text{SA} \approx 615.75216 \text{ cm}^2

  3. Round the surface area to 2 decimal places.

    SA=615.75 cm2\text{SA} = 615.75 \text{ cm}^2

    The surface area of the sphere is 615.75 cm2\boxed{\text{615.75 cm}^2}.

Part c

1436.76 cm3\text{1436.76 cm}^3

  1. Identify the radius.

    The radius is r=7r = 7 cm.

  2. Substitute the radius into the volume formula for a sphere.

    V=43πr3V = \frac{4}{3}\pi r^3 V=43×π×(7 cm)3V = \frac{4}{3} \times \pi \times (7 \text{ cm})^3 V=43×π×343 cm3V = \frac{4}{3} \times \pi \times 343 \text{ cm}^3 V=13723π cm3V = \frac{1372}{3}\pi \text{ cm}^3 V≈13723×3.14159265... cm3V \approx \frac{1372}{3} \times 3.14159265... \text{ cm}^3 V≈457.3333...×3.14159265... cm3V \approx 457.3333... \times 3.14159265... \text{ cm}^3 V≈1436.75504 cm3V \approx 1436.75504 \text{ cm}^3

  3. Round the volume to 2 decimal places.

    V=1436.76 cm3V = 1436.76 \text{ cm}^3

    The volume of the sphere is 1436.76 cm3\boxed{\text{1436.76 cm}^3}.

Part d

461.81 cm2\text{461.81 cm}^2

  1. Identify the radius.

    The radius is r=7r = 7 cm.

  2. Substitute the radius into the total surface area formula for a hemisphere.

    TSA of hemisphere=3πr2\text{TSA of hemisphere} = 3\pi r^2 TSA of hemisphere=3×π×(7 cm)2\text{TSA of hemisphere} = 3 \times \pi \times (7 \text{ cm})^2 TSA of hemisphere=3×π×49 cm2\text{TSA of hemisphere} = 3 \times \pi \times 49 \text{ cm}^2 TSA of hemisphere=147π cm2\text{TSA of hemisphere} = 147\pi \text{ cm}^2 TSA of hemisphere≈147×3.14159265... cm2\text{TSA of hemisphere} \approx 147 \times 3.14159265... \text{ cm}^2 TSA of hemisphere≈461.81412 cm2\text{TSA of hemisphere} \approx 461.81412 \text{ cm}^2

  3. Round the total surface area to 2 decimal places.

    TSA of hemisphere=461.81 cm2\text{TSA of hemisphere} = 461.81 \text{ cm}^2

    The total surface area of the hemisphere is 461.81 cm2\boxed{\text{461.81 cm}^2}.

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