Question

Total surface area of cone is 22m it's slant height is 6times the radius of base . find diameter of base
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Answer 1

Given:

• TSA of Cone = 22 m
• Slant height = 6 × Radius

To find:

1. Diameter of base = ?

Method:

$\large{\bf{\underline{FORMULA \: USED}}: TSA = \pi \times r(l+r)}\\\\\\:\implies \sf{22 = \pi \times r (6r+r)}\\\\\\:\implies \sf{22 = \dfrac{22}{7} \times r \times 7r}\\\\\\:\implies \sf{22 = \dfrac{22}{\not7} \times r \times \not7r}\\\\\\:\implies \sf{22 = 22 r^{2} }\\\\\\:\implies \sf{r^{2} = \dfrac{22}{22} }\\\\\\:\implies \sf{r^{2} = 1}\\\\\\:\implies \sf{r = \sqrt{1} }\\\\\\:\implies \sf{r = \pm 1} \\\\\\(Radius \: cannot \: be \: negative)\\\\\bf{\therefore \:Radius= 1m}$

$\rm{Diameter = 2 \times Radius}\\\\:\implies \sf{Diameter = 2(1)}\\\\:\implies \boxed{\boxed{\bf{Diameter = 2 m}}}$