Question

The curved surface area and total surface area of a cone
are 2200 cm² and 2816 cm respectively. Find the slant
height of the cone. step by step plz​

Answer 1

Answer:

50 cm

Step-by-step explanation:

πrl = 2200

πr(r+l) = 2816

or, πr^2 +πrl =2816

or, πr^2 + 2200 = 2816

or, πr^2 = 2816 - 2200

= 616

or,

$\frac{22}{7} {r}^{2} = 616 \\ {r}^{2} = 28 \times 7 \\ r = \sqrt{28 \times 7} = 2 \times 7 = 14$

πrl = 2200

$\frac{22}{7} \times 14 \times l = 2200 \\ l = 50$

Slant height = 50 cm

Answer 2

In the above question the curved surface area and total surface area of a cone are given and it is asked to find the slant height of the cone and for that here is the answer:-

Curved Surface Area = 2200 cm^2

πrl = 2200 cm^2 -(1)

Total Surface Area = 2816 cm^2

πr(l+r) = 2816 cm^2

πrl+πr^2 = 2816 cm^2 -(2)

From eq.(1) and (2):-

2200+πr^2 = 2816

πr^2 = 2816-2200

πr^2 = 616 cm^2

r^2 = 616×7/22

r = √196

r = 14 cm

π×14×l = 2200

l = (2200×7)÷(4×22)

l = 50 cm

Slant height = 50 cm

Hope this answer will help you.

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