Question

Surface area of a cone is 188.4 sq.cm and its slant height is 10cm. Find its perpendicular height.( Using 3.14)

Answer 1

$\large \bigstar\boxed{\bf \red{ GIVEN}} \bigstar \\ \\ \Longrightarrow \bf lateral \: surface \: area = 188.4 \: {cm}^{2} \\ \\\Longrightarrow \bf Slant \: height\: ( l ) = 10 \: cm$

$\large \bigstar\boxed{\bf \red{TO FIND}} \bigstar \\ \\\Longrightarrow \bf Height \: of \: the \: cone$

$\large \bigstar\boxed{\bf \red{SOLUTION}} \bigstar \\ \\ \large\boxed{ \bf \green{ L.S.A \: of \: cone = \pi rl }} \\ \\\Longrightarrow \bf 188.4 = 3.14 \times r \times 10 \\ \\\Longrightarrow \bf r = \frac{188.4}{31.4} \\ \\ \large \boxed{ \bf \orange{ r = 6 \: cm}}$

$\bf By \: using \: Pythagoras \: Theorem \\ \\ \boxed {\bf{ {h}^{2} = {p}^{2} + {b}^{2} }} \\ \\ \bf{10}^{2} = {p}^{2} + {6}^{2} \\ \\ \bf{p}^{2} = 100 - 36 \\ \\ \bf p = \sqrt{64} \\ \\ \boxed{ \bf \blue{ p = 8 \: cm}}$

Height of cone is 8 cm

Answer 2

Answer:

radius = r

slant hieght = 10cm

hieght = ?

surface area = 188.4cm²

surface area of cone = πrl

             188.4            = 3.14 x r x 10 

            188.4 / 31.4   = r

                radius        = 6cm

       l² = r² + h²

      10² = 6² + h²

     100 - 36 = h²

       √64 = h

       h = 8cm

therefore, the perpendicular hieght of cone is 8 cm

hope this may help u✌✌