Question

If curved surface area of a cone is 616 cm^2 and sla t height is 14 cm then find the Total surface area of the cone​

Answer 1

Answer:

Answer is in the pic.....

Answer 2

GIVEN :-

• Curved surface area of the cone = 616 cm²
• Slant height = 14 cm

TO FIND :-

• The total surface area of the cone

SOLUTION :-

Now , Curved surface area (CSA) of a cone is given by ;

$\\ \star\:\boxed{\sf{\purple{CSA=\pi rl}}}$

Where ,

• r is radius of the cone
• l is slant height of the cone

Substituting the values ,

$\\ : \implies \sf \: 616 = \frac{22}{7} \times r \times 14$

$\\ : \implies \sf \: 616 = 22 \times 2 \times r$

$\\ : \implies \sf \: 616 = 44 \times r$

$\\ : \implies \sf \: \frac{616}{44} = r$

$\\ : \implies {\boxed{\red{\mathfrak{r = 14 \: cm}}}}$

Now , Total surface (TSA) of a cone is given by ,

$\\ \star \: \boxed{\purple{\sf{TSA = \pi r(l+r)}}}$

Substituting the values ,

$\\ :\implies \sf \: TSA = \frac{22}{7} \times 14(14 + 14)$

$\\ : \implies \sf \:TSA = 22 \times 2(14 +14)$

$\\ : \implies \sf \: TSA = 44(14 + 14)$

$\\ : \implies \sf \:TSA = 44(28)$

$\\ : \implies {\boxed{\pink{\sf{TSA = 1232 \: cm {}^{2} }}}} \: \bigstar$

Hence , The Total surface are of the cone is 1232 cm².