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    A cylinder has a radius of 8π\frac{8}{\pi}π8​ cm and its volume is 448 cm3^33. What is the height of the cylinder (take π\piπ = 227\frac{22}
    Question

    A cylinder has a radius of 8π\frac{8}{\pi} cm and its volume is 448 cm3^3. What is the height of the cylinder (take π\pi = 227\frac{22}{7}​)?​

    A.

    21 cm

    B.

    23 cm

    C.

    22 cm

    D.

    24 cm

    Correct option is C

    Given:
    Radius r = 8π\frac{8}{\pi}​ cm

    Volume of the cylinder = 448 cm³

    π=227\pi = \frac{22}{7}

    Formula Used:

    Volume of a cylinder is given by the formula:

    V = πr2h \pi r^2 h

    where r is the radius and h is the height.​​

    Solution:

    V = 448 cm³, r = 8π\frac{8}{\pi}​ cm, and π=227\pi = \frac{22}{7}​​

    448 = π×(8π)2×h\pi \times \left(\frac{8}{\pi}\right)^2 \times h​​

    448 = π×64π2×h\pi \times\frac{64}{\pi^2} \times h​​

    448 = 64π×h\frac{64}{\pi} \times h

    h × 64\times \space 64 = 448 ×π448\space \times \pi​​

    h =  7 π\pi

    h = 7 × 227\times \space \frac{22}{7}

    h = 22 cm

    Thus, the correct option is (c) 22 cm.


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