Let's solve each problem step by step:
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Volume of the oblique cylinder (height = 15 cm, radius = 5 cm): \[ \text{Volume} = \pi r^2 h = 3.14 \times (5^2) \times 15 = 3.14 \times 25 \times 15 = 3.14 \times 375 = 1177.5 \text{ cm}^3 \] Response: 1177.5 cubic centimeters
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Surface area of the cylinder (radius = 4 ft, height = 3 ft): \[ \text{Surface Area} = 2\pi r(h + r) = 2 \times 3.14 \times 4(3 + 4) = 2 \times 3.14 \times 4 \times 7 = 2 \times 3.14 \times 28 = 176.96 \text{ ft}^2 \] Rounding to the nearest tenth: 177.0 ft²
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Surface area of the cone (diameter = 14 inches, slant height = 20 inches; radius = 7 inches): \[ \text{Surface Area} = \pi r (l + r) = 3.14 \times 7(20 + 7) = 3.14 \times 7 \times 27 \] \[ = 3.14 \times 189 = 592.86 \text{ in}^2 \] Rounding to the nearest hundredth: 592.86 square inches
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Volume of the cylinder (radius = 8 mm, height = 13 mm): \[ \text{Volume} = \pi r^2 h = 3.14 \times (8^2) \times 13 = 3.14 \times 64 \times 13 = 3.14 \times 832 = 2611.68 \text{ mm}^3 \] Rounding to the nearest hundredth: 2611.68 cubic millimeters
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Volume of the water bottle (height = 16 inches, radius = 4 inches): \[ \text{Volume} = \pi r^2 h = 3.14 \times (4^2) \times 16 = 3.14 \times 16 \times 16 = 3.14 \times 256 = 804.64 \text{ in}^3 \] Rounding to the nearest hundredth: 804.64 cubic inches
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Volume of the cone (radius = 13 inches, height = 27 inches): \[ \text{Volume} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.14 \times (13^2) \times 27 = \frac{1}{3} \times 3.14 \times 169 \times 27 \] \[ = \frac{1}{3} \times 3.14 \times 4563 = 4780.66 \text{ in}^3 \] Rounding to the nearest hundredth: 4780.66 cubic inches
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Volume of the cone-shaped container (radius = 4 feet, height = 12 feet): \[ \text{Volume} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.14 \times (4^2) \times 12 = \frac{1}{3} \times 3.14 \times 16 \times 12 \] \[ = \frac{1}{3} \times 3.14 \times 192 = 201.06 \text{ ft}^3 \] Rounding to the nearest hundredth: 201.06 cubic feet
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Diameter of a sphere responses: Response: is the longest distance on a sphere.
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Surface area of a hemisphere (radius = 10 m): \[ \text{Surface Area} = 2\pi r^2 + \pi r^2 = 3\pi r^2 = 3\pi (10^2) = 300\pi \text{ m}^2 \] Response: 300π m²
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Radius of the sphere (surface area = 7.84π ft²): \[ 4\pi r^2 = 7.84\pi \implies r^2 = \frac{7.84}{4} = 1.96 \implies r = \sqrt{1.96} = 1.4 \text{ ft} \]
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Volume of the spherical scoop of ice cream (radius = 3 cm): \[ \text{Volume} = \frac{4}{3} \pi r^3 = \frac{4}{3} \times 3.14 \times (3^3) = \frac{4}{3} \times 3.14 \times 27 \] \[ = \frac{4 \times 84.78}{3} = \frac{339.12}{3} = 113.04 \text{ cm}^3 \] Rounding to nearest whole number: 113 cm³
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Relationship between sphere, cylinder, and cone volumes: Response: 1 cylinder = 2 cones + 1 sphere
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Volume of the cylinder (same radius as sphere, height = diameter of sphere): \[ V_s = 48 \text{ m}^3 \implies \frac{4}{3}\pi r^3 = 48 \implies r^3 = \frac{48 \cdot 3}{4\pi} = \frac{144}{\pi}, \quad h = 2r \] The volume of the cylinder: \[ V_c = \pi r^2 h = \pi r^2 (2r) = 2\pi r^3 = 2 (48) = 96 \text{ m}^3 \] Thus, the volume of the cylinder is 96 m³.
If you have any specific question you want to clarify, feel free to ask!