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Pranay Kumar Misra
Asked: 2022-11-08T06:07:39+05:30 In:

In a right angle, the sides conrtaining right angles are 5 cm and 12 cm. It is rotated aboutits hypotenuse taking it as axis. Find the total surface area and volume of formed figure.
image

In a right angle, the sides conrtaining right angles are 5 cm and 12 cm. It is rotated aboutits hypotenuse taking it as axis. Find the total surface area and volume of formed figure.
image
Parabola
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  1. Let `Delta ABC` is given in which
    AB = 5cm
    BC = 12cm
    and `angleABC= 90^(@)`
    Now, from Phythagoarstheorem
    `AC^(2)=AB^(2)+BC^(2)`
    `=5^(2)+12^(2)`
    = 25 + 144 = 169
    `rArr AC=13cm`
    Let BO = r
    Now, area of `Delta ABC =(1)/(2)xxABxxBX=(1)/(2)xx5xx12`
    Again, area of `Delta ABC = (1)/(2)xxACxxBO=(1)/(2)xx13xx r`
    `therefore (1)/(2)xx13xx r=(1)/(2)xx5xx12`
    `rArr r = (60)/(13) cm`
    Now, the volume of solid = volume of cone ABD + volume of cone CBD
    `=(1)/(3)pi r^(2)xxAO+(1)/(3)pi r^(2)xxOC=(1)/(3)pi r^(2)(AO+OC)`
    `=(1)/(3)pi r^(2)xxAC=(1)/(3)xx pi xx(60)/(13)xx(60)/(13)xx13=(1200pi)/(13)cm^(3)`
    and total surface area = curved surface of cone ABD + curved surface of cone CBD
    `= pi r(AB)+ pi r(BC)`
    `= pi r(AB+BC)`
    `= pi xx(60)/(13)(5+12)`
    `=(1020pi)/(13)cm^(2)`

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