Question

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The radius and height of the cone are in the ratio 4:3 .The area of the base is 154cm^2. find TSA.

Answer 1

let the radius be 4x and height be 3x


Base of cone is a circle

$area \: of \: base \: = \pi {r}^{2} \\ \frac{22}{7 } \times {r}^{2} = 154 \\ r = 7 \\ 4x = 7 \\ x = \frac{7}{4} \\ height \: = 3x = 3 \times \frac{7}{4} \\ = \frac{21}{4} \\ total \: surface \: area \: \\ = \pi \times r(l + r) \\ l = \sqrt{ {r}^{2} + {h}^{2} } \\ l = \frac{35}{4} \\ \frac{22}{7} \times 7( \frac{35}{4} + 7) \\ 22 \times \frac{63}{4} \\ = 346.5$