Ex.13.3 Q3 Surface Areas and Volumes Solution - NCERT Maths Class 9

Go back to  'Ex.13.3'


Curved surface area of a cone is \(\begin{align}308\,\,c{m^2} \end{align}\) and its slant height is \(14\rm\, cm.\) Find

(i) Radius of the base

(ii) Total surface area of the cone.

Text Solution


The total surface area of the cone is the sum of the curved surface area and its base area which is a circle.

What is known?

Curved surface area of the cone and its slant height.

What is unknown?

(i) Radius of the base.


Curved surface area \(=\) \(\begin{align}\,\,\pi rl = 308\,\,{\rm{cm}}^2 \end{align}\)

Slant height (\(l\)) \(= 14\,\rm cm\)

\[\begin{align}\pi rl &= 308 \\\frac{{22}}{7} \times r \times 14 &= 308 \\r &= \frac{{308}}{{14}} \times \frac{7}{{22}} = 7\,\,\rm cm\end{align}\] 

(ii) Total surface area of the cone.


Total surface area \(\begin{align}\, = \pi r\,(l + r) \end{align}\)

Radius \(= 7 \rm\,cm\)

Slant height (\(l\)) \(= 14\,\rm cm\)

\[\begin{align}\rm TSA &= \pi r(r + l) \\ &= \frac{{22}}{7} \times 7 \times (7 + 14) \\ &= 22 \times 21 \\ & = 462\,\,\rm c{m^2} \end{align}\]


Radius of the cone \(= 7\,\rm cm\)

Total surface area of the cone \( = 462\, \rm cm^2 \)

Learn from the best math teachers and top your exams

  • Live one on one classroom and doubt clearing
  • Practice worksheets in and after class for conceptual clarity
  • Personalized curriculum to keep up with school