Find the curved surface area and the total surface area of a cone with radius $3.5 \, cm$ and height $12 \, cm$.
(N/A) Given: Radius $(r) = 3.5 \, cm$,Height $(h) = 12 \, cm$.
First,find the slant height $(l)$ using the formula $l = \sqrt{r^2 + h^2}$.
$l = \sqrt{(3.5)^2 + (12)^2} = \sqrt{12.25 + 144} = \sqrt{156.25} = 12.5 \, cm$.
Curved Surface Area $(CSA) = \pi rl = \frac{22}{7} \times 3.5 \times 12.5 = 22 \times 0.5 \times 12.5 = 137.5 \, cm^2$.
Total Surface Area $(TSA) = \pi r(r + l) = \frac{22}{7} \times 3.5 \times (3.5 + 12.5) = 22 \times 0.5 \times 16 = 11 \times 16 = 176 \, cm^2$.
First,find the slant height $(l)$ using the formula $l = \sqrt{r^2 + h^2}$.
$l = \sqrt{(3.5)^2 + (12)^2} = \sqrt{12.25 + 144} = \sqrt{156.25} = 12.5 \, cm$.
Curved Surface Area $(CSA) = \pi rl = \frac{22}{7} \times 3.5 \times 12.5 = 22 \times 0.5 \times 12.5 = 137.5 \, cm^2$.
Total Surface Area $(TSA) = \pi r(r + l) = \frac{22}{7} \times 3.5 \times (3.5 + 12.5) = 22 \times 0.5 \times 16 = 11 \times 16 = 176 \, cm^2$.
Explore More
Similar Questions
The radius of a cone is $15 \, cm$ and its slant height is $25 \, cm$. Find the curved surface area and the total surface area of the cone. $(\pi = 3.14)$
Medium
View SolutionFind the total surface area of a cone with diameter $6\, cm$ and slant height $11\, cm$. (in $cm^2$)
Easy
View SolutionIn $\triangle ABC$,$\angle B = 90^{\circ}$,$AB = 28 \, cm$,and $BC = 21 \, cm$. If the triangle is revolved about the side $AB$,find the curved surface area of the cone so obtained. Similarly,if the triangle $ABC$ is revolved about the side $BC$,find the curved surface area of the cone so obtained.
Medium
View Solution$A$ corn cob (see figure),shaped somewhat like a cone,has the radius of its broadest end as $2.1\, cm$ and length (height) as $20\, cm$. If each $1\, cm^2$ of the surface of the cob carries an average of four grains,find how many grains you would find on the entire cob.
Medium
View SolutionWhat length of tarpaulin $3\, m$ wide will be required to make a conical tent of height $8\, m$ and base radius $6\, m$ (in $, m$)? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately $20\, cm$ (Use $\pi = 3.14$).
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo