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The curved surface area of a right cylinder is 3696 cm2. Its height is three times its radius. What is the capacity (in liters) of the cylinder? $$\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)$$
Answer & Solution
Correct Answer:
Option
A
$$\eqalign{
& r:h = 1:3 \cr
& 2\pi rh = 3696 \cr
& 2 \times \frac{{22}}{7} \times x \times 3x = 3696 \cr
& 3{x^2} = \frac{{3696 \times 7}}{{44}} \cr
& {x^2} = \frac{{1232 \times 7}}{{44}} \cr
& {x^2} = \frac{{112 \times 7}}{4} \cr
& {x^2} = 28 \times 7 \cr
& x = 14 \cr
& {\text{Volume}} = \pi {r^2}h \cr
& = \frac{{22}}{7} \times {14^2} \times 42 \cr
& = \frac{{22}}{7} \times 14 \times 14 \times 42 \cr
& = 25872{\text{ c}}{{\text{m}}^3} \cr
& = 25.872{\text{ L}} \cr} $$
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