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 Mensuration: Cylinder, Cone and Sphere 30 Flashcards |
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A cylinder has a curved surface area of 2πrh. If the height is 20 cm and the radius is 5 cm, what is the curved surface area? |
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 Curved surface area = 2πrh = 2 × π × 5 × 20 = 200π cm². |
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The volume of a cone is given by (1/3)πr²h. Calculate the volume of a cone with a radius of 3 cm and a height of 9 cm. |
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 Volume = (1/3)π(3)²(9) = 27π cm³. |
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True or False: The total surface area of a sphere is calculated using the formula 4πr. |
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 False. The total surface area of a sphere is calculated using the formula 4πr². |
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Fill in the blank: The volume of a hollow cylinder is calculated using the formula ___ = (4/3)π(R³ - r³). |
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 Volume |
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If a sphere has a radius of 7 cm, what is its volume? |
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 Volume = (4/3)π(7)³ = (4/3) × π × 343 = 1,436.76 cm³. |
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Which formula would you use to find the total surface area of a hemisphere? |
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 Total surface area = 3πr². |
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A hollow sphere's internal radius is 2 cm and external radius is 4 cm. What is its volume? |
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 Volume = (4/3)π(4³ - 2³) = (4/3)π(64 - 8) = (4/3)π(56) = 234.93 cm³. |
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Calculate the total surface area of a cone with radius 6 cm and slant height 10 cm. |
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 Total surface area = πr(l + r) = π(6)(10 + 6) = 96π cm². |
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True or False: The curved surface area of a cylinder is found using the formula 2πr². |
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 False. The curved surface area of a cylinder is found using the formula 2πrh. |
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A cylinder has a radius of 5 cm and a height of 10 cm. What is its volume? |
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 Volume = πr²h = π(5)²(10) = 250π cm³. |
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If the external radius of a hollow cylinder is 6 cm and the internal radius is 4 cm, what is the thickness of the wall? |
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 Thickness = R - r = 6 - 4 = 2 cm. |
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Fill in the blank: The formula for the volume of a hemisphere is ___ = (2/3)πr³. |
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 Volume |
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What is the formula for calculating the circumference of a circle? |
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 Circumference = 2πr. |
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A cone with a radius of 4 cm and height of 12 cm has a slant height calculated as l = √(r² + h²). What is l? |
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 L = √(4² + 12²) = √(16 + 144) = √160 = 4√10 cm. |
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If a cylindrical tank has a height of 5 m and a radius of 2 m, what is the curved surface area? |
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 Curved surface area = 2πrh = 2π(2)(5) = 20π m². |
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