Question

csa of a cone is 550 sq cm and tea of the cone is 704 sq cm find radius​

Answer 1

ANSWER :

Radius of the cone is 7 cm.

EXPLANATION :

GIVEN :-

• CSA of cone = 550 cm²
• TSA of cone = 704 cm²

TO FIND:-

• Radius of the cone.

SOLUTION :-

Let the radius of the cone be r cm.

Formulas Used :-

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

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

Where,

r = Radius

l = Slant height

According to the question,

$\sf{\pi\:rl=550..........(i)}$

$\sf{\pi\:r(r+l)=704........(ii)}$

✪ Now taking eq(ii) ✪

$\sf{\pi\:r(r+l)=704}$

$\implies\sf{\pi\:r^2+\pi\:rl=704}$

$\implies\sf{\frac{22}{7}r^2+550=704\:[putting\:\pi\:rl=550\: from\:eq(i)}$

$\implies\sf{\frac{22}{7}r^2=704-550}$

$\implies\sf{\frac{22}{7}r^2=154}$

$\implies\sf{r^2=154\times\frac{7}{22}}$

$\implies\sf{r^2=7\times\:7}$

$\implies\sf{r=7}$

Therefore, radius of the cone is 7 cm.

___________________________

MORE INFORMATION :

✪ Volume of cone =1/3 πr²h

✪ Volume of cylinder = πr²h

✪ CSA of cylinder = 2πrh

✪ TSA of cylinder = 2πr(h+r)

_____________________________

Answer 2

$\huge \mathfrak{Answer:-}$

$\implies$ r = 7

$\large\underline\mathrm{Given:-}$

• CSA of cone = 550cm²
• TSA of cone = 704cm²

$\large\underline\mathrm{To \: find}$

• Radius of the cone.

$\large\underline\mathrm{Solution}$

• Let the radius of the cone be r cm.

$\large\underline\mathrm{Formulas \: used}$

$\large\underline\mathrm{A/Q}$

$\implies$ πrl = 550_____(1)

$\implies$ πr(r + l)______(2)

$\large\underline\mathrm{Now, \: Eq. ___(1)}$

$\implies$ πr(r + l) = 704

$\implies$ πrl + πr² = 704

$\implies$ 22/7r² + 550 = 704

$\implies$ 22/7r² = 704 - 550

$\implies$ 22/7r² = 154

$\implies$ 22/7r² =

$\implies$ r² = 154 × 7/22

$\implies$ r² = 7 × 7

$\implies$ r = 7

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{radius \: of \: the \: cone \: is \: 7cm.}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$