Question

Curved surface area of a cone is 308 cm and its slant height is 14 cm. Find
(i) radius of the base and (ii) total surface area of the cone.​

Answer 1

Answer:

L=14

CSA of cone = 308

$\pi \times r \times l = 308 \\ \frac{22}{7} \times r \times 14 = 308 \\ r = \frac{308}{14} \times \frac{7}{22} \\ = 7$

$tsa \: of \: cone = \pi \times r(r + l) \\ = \frac{22}{7} \times 7(7 + 14) \\ = 22 \times 21 \\ = 462$

Answer 2

Answer:

Answer :

• ➠ (i) The radius of the base of cone is 7 cm.
• ➠ (ii) Total surface area of cone is 462 cm².

$\begin{gathered}\end{gathered}$

Given :

• ➠ (i) Curved surface area of a cone is 308 cm.
• ➠ (ii) Slant height of cone is 14 cm.

$\begin{gathered}\end{gathered}$

To Find :

• ➠ (i) radius of the base and
• ➠ (ii) total surface area of the cone.

$\begin{gathered}\end{gathered}$

Using Formulas :

➠ $\small{\underline{\boxed{\sf{CSA \: of \: cone = \pi rl}}}}$

➠ $\small{\underline{\boxed{\sf{TSA \: of \: cone = \pi r (r + l )}}}}$

Where :-

• ➯ CSA = Curved surface area
• ➯ TSA = Total surface area
• ➯ π = 22/7
• ➯ r = radius
• ➯ h = height

$\begin{gathered}\end{gathered}$

Solution :

Finding the radius of cone by substituting the values in the formula :-

$\dashrightarrow{\sf{CSA \: of \: cone = \pi rl}}$

$\dashrightarrow{\sf{308= \dfrac{22}{7} \times r \times 14}}$

$\dashrightarrow{\sf{308= \dfrac{22}{\cancel{7}} \times r \times \cancel{14}}}$

$\dashrightarrow{\sf{308= 22 \times r \times 2}}$

$\dashrightarrow{\sf{308= 44 \times r}}$

$\dashrightarrow{\sf{308= 44r}}$

$\dashrightarrow{\sf{r = \dfrac{308}{44}}}$

$\dashrightarrow{\sf{r = \cancel{\dfrac{308}{44}}}}$

$\dashrightarrow{\sf{r = 7 \: cm}}$

$\bigstar \: \underline{\boxed{\sf{\purple{ Radius= 7 \: cm}}}}$

∴ The radius of cone is 7 cm.

$\rule{300}{1.5}$

Now, finding TSA of cone by substituting the values in the formula :-

$\dashrightarrow{\sf{TSA \: of \: cone = \pi r (r + l )}}$

$\dashrightarrow{\sf{TSA \: of \: cone = \dfrac{22}{7} \times 7(7 + 14)}}$

$\dashrightarrow{\sf{TSA \: of \: cone = \dfrac{22}{\cancel{7}} \times \cancel{7}(21)}}$

$\dashrightarrow{\sf{TSA \: of \: cone = 22 (21)}}$

$\dashrightarrow{\sf{TSA \: of \: cone = 22 \times 21}}$

$\dashrightarrow{\sf{TSA \: of \: cone = 462 \: {cm}^{2} }}$

$\bigstar \: \underline{\boxed{\sf{\purple{TSA \: of \: cone = 462 \: {cm}^{2}}}}}$

∴ The total surface area of cone is 462 cm².

$\begin{gathered}\end{gathered}$

Learn More :

$\boxed{\begin{minipage}{6 cm}\bigstar \:\underline{\textbf{Formulae Related to Cone :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area = \pi rl\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:TSA = Area\:of\:Base + CSA=\pi r^2+\pi rl\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\dfrac{1}{3}\pi r^2h\\ \\{\textcircled{\footnotesize\textsf{5}}} \: \:Slant \: Height=\sqrt{r^2 + h^2}\end{minipage}}$

$\underline{\rule{220pt}{2.5pt}}$