ack":"To avoid losing accuracy, rounding should only be performed at the end of the calculation.","points":null},{"id":"b2f72f79-6549-43cc-bff9-b916c986116b","cardType":"basic","front":"Which measurement of a cone is used to calculate its volume?","back":"The vertical height ($h$).","points":1},{"id":"5ac750cc-1c85-4f9f-9f50-b1b56d4f04b5","cardType":"basic","front":"Which measurement of a cone is used to calculate its curved surface area?","back":"The slant height ($l$).","points":1},{"id":"3f94a89c-b229-4179-9f45-1878ef25afd2","cardType":"cloze","front":"The volume of a cone is calculated using the formula $V = \\text{[...]}$.","back":"The volume of a cone is calculated using the formula $V = \\boxed{\\frac{1}{3}\\pi r^2 h}$.","points":null},{"id":"3a226d99-f6fb-4c13-aac8-4f723681c30d","cardType":"cloze","front":"The volume of a sphere is calculated using the formula $V = \\text{[...]}$.","back":"The volume of a sphere is calculated using the formula $V = \\boxed{\\frac{4}{3}\\pi r^3}$.","points":null},{"id":"305d213b-167f-48e7-b4bd-6dadfbba4e07","cardType":"basic","front":"What is the volume of a hemisphere in terms of $r$?","back":"$$\\frac{2}{3}\\pi r^3$","points":1},{"id":"8c60f254-ed80-44b3-b534-4bae336d7f84","cardType":"basic","front":"What does the formula $\\pi rl$ represent for a cone?","back":"The curved surface area.","points":1},{"id":"681c8362-35bf-4426-82e4-9e406d5e226c","cardType":"basic","front":"How is the total surface area of a solid cone calculated?","back":"

Curved surface area ($\\pi rl$)
Base area ($\\pi r^2$)

","points":2},{"id":"8925e289-0200-450f-83ee-03ba73973187","cardType":"basic","front":"What is the surface area of a sphere?","back":"$$4\\pi r^2$","points":1},{"id":"d64365b0-75a9-4e72-86ee-52e06571ac71","cardType":"cloze","front":"The total surface area of a solid hemisphere is $\\text{[...]}$.","back":"The total surface area of a solid hemisphere is $\\boxed{3\\pi r^2}$.","points":null},{"id":"2f96571f-9c4c-4ecb-8335-b0b47c56087e","cardType":"basic","front":"Why does a solid hemisphere have a total surface area of $3\\pi r^2$?","back":"It combines the curved surface ($2\\pi r^2$) and the flat circular base ($\\pi r^2$).","points":2},{"id":"4a3f0a41-60d2-46fd-b089-e5689a7b013d","cardType":"cloze","front":"In a cone, the relationship between slant height ($l$), vertical height ($h$), and radius ($r$) is $\\text{[...]}$.","back":"In a cone, the relationship between slant height ($l$), vertical height ($h$), and radius ($r$) is $\\boxed{l^2 = h^2 + r^2}$.","points":null},{"id":"dbdd4d08-2a38-4930-8065-d6144310bae3","cardType":"basic","front":"What theorem is used to find the slant height of a cone if only the vertical height and radius are known?","back":"Pythagoras' theorem.","points":1},{"id":"09434e4c-f110-4dd4-9f62-75af15d7b045","cardType":"basic","front":"How do you calculate the total volume of a compound solid?","back":"Add the volumes of the individual shapes together.","points":1},{"id":"ada11926-cba6-4476-a71a-330f29024c58","cardType":"basic","front":"What does it mean to give an answer \"in terms of $\\pi$\"?","back":"Leave the symbol $\\pi$ in the final answer instead of converting to a decimal.","points":1},{"id":"3fb90556-05d1-41fe-ba99-08156e130266","cardType":"cloze","front":"When a solid is fully submerged, the rise in water level = $\\text{[...]}$.","back":"When a solid is fully submerged, the rise in water level = $\\boxed{\\frac{\\text{volume of solid}}{\\text{area of container base}}}$.","points":null},{"id":"37d9d04e-b9ca-4f73-9ef0-8f17662e927c","cardType":"basic","front":"How does the volume of a submerged solid relate to the water it displaces?","back":"The volume of the solid equals the volume of the water displaced.","points":1},{"id":"781faf28-9c1b-402f-a292-05493330cc72","cardType":"basic","front":"What operation is used to find the radius of a sphere if the volume is known?

Spheres and Cones Flashcards

Spheres and Cones Flashcards

Spheres and Cones Flashcards

Spheres and Cones Flashcards