GCSE Mathematics (9-1)
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    19.5 Surface area and volume of spheres, cones and pyramids — Practise with help

    Warm-up: remember

    1. Find the area of a circle with radius 3 cm. 2. A prism has cross-section area AA and length hh. State its volume.
    Check your answers
    1. 9π cm29\pi\text{ cm}^2. 2. AhAh.

    Practise with help

    Attempt each question first. Open the hint, then the next step, when needed.

    1. A ball has radius 4 cm. Work out its surface area in terms of π.

    Hint

    Sphere surface area is 4πr24\pi r^2.

    Next step

    Substitute r=4r=4 cm and evaluate 424^2.

    Full working

    A=4π×42=4π×16=64π cm2A=4\pi\times4^2=4\pi\times16=64\pi\text{ cm}^2.

    2. A cone has radius 4 cm and perpendicular height 9 cm. Work out its volume in terms of π.

    Hint

    Cone volume is one third of the circular base area multiplied by the perpendicular height.

    Next step

    Substitute r=4r=4 cm and h=9h=9 cm into V=13πr2hV=\frac13\pi r^2h.

    Full working

    V=13π×42×9=48π cm3V=\frac13\pi\times4^2\times9=48\pi\text{ cm}^3.

    3. A square-based pyramid has base side 5 cm and perpendicular height 6 cm. Work out its volume.

    Hint

    Pyramid volume is one third of the base area multiplied by the perpendicular height.

    Next step

    Find the square base area first: 5×5=25 cm25\times5=25\text{ cm}^2.

    Full working

    V=13×25×6=50 cm3V=\frac13\times25\times6=50\text{ cm}^3.

    Try the remaining questions without opening the full working.

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