er but the formula requires $r$?","back":"Halve the diameter to find the radius ($r = \\frac{d}{2}$).","points":1},{"id":"ba9f399b-f73d-4b4f-8659-6154ae633e24","cardType":"basic","front":"State the formula for the volume of a cone.","back":"$$V = \\frac{1}{3}\\pi r^2h$","points":1},{"id":"5d350d1a-7a50-471d-9b33-72e904ed5851","cardType":"basic","front":"State the formula for the curved surface area of a cone.","back":"$$A = \\pi rl$","points":1},{"id":"caafb946-175b-44f4-a068-17b944b15e59","cardType":"cloze","front":"In the formula for the curved surface area of a cone ($\\pi rl$), the symbol $l$ represents the [ ].","back":"In the formula for the curved surface area of a cone ($\\pi rl$), the symbol $l$ represents the slant height.","points":null},{"id":"a5d3d449-0540-4412-9e77-a96899b24ff7","cardType":"basic","front":"How do you calculate the slant height ($l$) of a cone if you only know the vertical height ($h$) and radius ($r$)?","back":"Use Pythagoras' Theorem: $l^2 = r^2 + h^2$.","points":2},{"id":"f386b1f7-0a24-42ea-b667-c6dce4fd7951","cardType":"basic","front":"What is the total surface area of a solid cone?","back":"

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

","points":2},{"id":"ffd65808-9869-4888-910f-76f94352f6e9","cardType":"basic","front":"Identify the difference between the vertical height and slant height of a cone.","back":"

Vertical height: distance from base centre to apex
Slant height: distance along the outside edge to apex

","points":2},{"id":"9f89f11a-6a9c-4046-8020-56824cfc1342","cardType":"cloze","front":"The formula for the volume of a sphere is $V = \\frac{4}{3}\\pi \\text{[...]}$.","back":"The formula for the volume of a sphere is $V = \\frac{4}{3}\\pi \\boxed{r^3}$.","points":null},{"id":"a169841b-9dd3-40c0-8094-85217869e811","cardType":"basic","front":"State the formula for the surface area of a sphere.","back":"$$A = 4\\pi r^2$","points":1},{"id":"874ae7a8-8f50-422a-b94f-b0e513a15bb3","cardType":"cloze","front":"A solid hemisphere has a total surface area of [ ].","back":"A solid hemisphere has a total surface area of $3\\pi r^2$.","points":null},{"id":"c5bb4837-0681-4c69-8538-ef31aba4fb7a","cardType":"basic","front":"What is the formula for the volume of a hemisphere?","back":"$$V = \\frac{2}{3}\\pi r^3$","points":1},{"id":"879b2024-b805-4cec-83b3-016588ffa77f","cardType":"basic","front":"Why is the total surface area of a solid hemisphere $3\\pi r^2$ rather than $2\\pi r^2$?","back":"It includes the curved surface ($2\\pi r^2$) plus the flat circular base ($\\pi r^2$).","points":2},{"id":"940c81a0-4fd6-4481-872c-96556945be5a","cardType":"basic","front":"When calculating the volume of a compound solid, what is the general rule?","back":"Add the volumes of the individual parts together.","points":1},{"id":"8dcd16a2-183a-4c55-8127-c03fe5480c9c","cardType":"basic","front":"When calculating the surface area of a compound solid, which faces are excluded?","back":"Joined faces (internal faces) are not counted; only outside faces are included.","points":1},{"id":"b0800123-a1ca-495a-b2fa-7e354492c828","cardType":"basic","front":"How should you handle rounding in multi-step calculations for cones and spheres?","back":"Round only at the final answer to avoid inaccuracy; keep the full calculator value until then.","points":1},{"id":"2a6bca46-c0cb-42a6-ad76-2b5a286c103c","cardType":"basic","front":"What does it mean t

Spheres and Cones Flashcards

Spheres and Cones Flashcards

Spheres and Cones Flashcards

Spheres and Cones Flashcards