Question

find the volume , CSA and TSA of a cone with the given radius 3 m and height 4m​

Answer 1

Answer:

$CSA=15\pi$ $m^{2}$ , $TSA = 24\pi$ $m^{2}$

Step-by-step explanation:

Radius$(r)$ = $3$ $m$

Height$(h)$ = $4$ $m$

Slant Height$(l)$ = $\sqrt{r^{2}+h^{2} }$

⇒$\sqrt{9 + 16}$

⇒$\sqrt{25}$

⇒±$5$

Since Distance cannot be negative

Slant Height$(l)$ = $5$ $m$

Curved Surface Area $(CSA)$ = $\pi r} l$ = $\frac{22}{7}*3*5$

⇒$15\pi$ $m^{2}$

Total Surface Area $(TSA)$ = $\pi rl+\pi r^{2}$

⇒$15\pi + 9\pi$

⇒$24\pi$ $m^{2}$

Answer 2

Step-by-step explanation:

volume of cone =

radius of cone = 3m

height of cone = 4m

$= \frac{1}{3} \pi {r}^{2} h \\ \frac{1}{3} \times \frac{22}{7} \times 3 \times 3 \times 4 \\ \frac{22}{7} \times 12 \\ 37.714 \: {m}^{3}$

Csa of cone =

radius of cone = 3m

height of cone = 4m

$l = \sqrt{ {r}^{2} + {h}^{2} } \\ l = \sqrt{ {3}^{2} + {4}^{2} } \\ l = \sqrt{9 + 16} \\ l = \sqrt{25} \\ l = 5m \\ csa \: of \: cone \: = \pi \: rl \\ = \frac{22}{7} \times 3 \times 5 \\ = 47.142 {m}^{2}$

Tsa of cone =

radius of cone = 3m

height of cone (L) = 5m

$= \pi \: r(r + l) \\ = \frac{22}{7} \times 3 (3 + 5) \\ = \frac{66}{7} (8m) \\ = 75.428 {m}^{2}$

i hope it will help you buddy .