Question

If the total surface area of a cone is 594cm^2 and its slant height is 20cm, find the radius of it circular base.

Ans: 7

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• Total surface area of a cone is 594 cm²

• Slant height of the cone is 20 cm.

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• The radius of base

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

We know that ,

$\:\:$

$\underline{\bold{\texttt{Total surface area of cone :}}}$

$\:\:$

➠ S = πr(r + L) ⚊⚊⚊⚊ ⓵

$\:\:$

Where ,

$\:\:$

• S = Total surface area

• r = Radius

• L = Slant height

$\:\:$

$\underline{\bold{\texttt{Total surface area of given cone :}}}$

$\:\:$

• S = 594 cm²

• r = r

• L = 20 cm

$\:\:$

⟮ Putting the values in ⓵ ⟯

$\:\:$

➜ S = πr(r + L)

$\:\:$

➜ $\sf 594 = \dfrac { 22 } { 7 } r (r + 20)$

$\:\:$

➜ $\sf \dfrac { 594 \times 7 } { 22 } = r(r + 20)$

$\:\:$

➜ $\sf 27 \times 7 = r^2 + 20r$

$\:\:$

➜ $\sf r ^2 + 20r = 189$

$\:\:$

➜ r² + 20r - 189 = 0

$\:\:$

➜ r² + 27r - 7r - 189 = 0

$\:\:$

➜ r(r + 27) -7(r + 27) = 0

$\:\:$

➜ (r + 27)(r - 7) = 0

$\:\:$

• r = -27
• r = 7

$\:\:$

As radius can't be negative

$\:\:$

Thus ,

$\:\:$

➜ r = 7

$\:\:$

• Hence the radius of cone is 7 cm

Answer 2

SOLUTION:

━━━━━━━━━━━━━━━━━━━━━━━━━━

ANSWER:-

Radius = 7cm

GIVEN:-

Total surface area of cone = 594cm²

Slant height ( l ) = 20cm

TO FIND:-

radius of circular base.

SOLUTION:-

Let the radius be r

FORMULA TO FIND RADIUS:

T.S.A of cone = πr( l + r)

SOLVING BY APPLYING THE FORMULA:-

↦ 594 = $\sf \dfrac{22}{7}$r ( 20 + r)ㅤ

↦594 × $\sf \dfrac{7}{22}$ = r(20 + r)

↦27 × 7 = 20 r + r²

↦189 = 20r + r²

↦r² + 20r - 189 = 0

↦r² + 27r - 7r - 189 = 0

↦r (r+ 27) - 7(r + 27) = 0

↦ ( r - 7) (r + 27) = 0

↦ r = 7 , -27

↦r = 7 cm

Hence, radius of circular cone = 7cm.

━━━━━━━━━━━━━━━━━━━━━━━━━━