Question

batao surface area of right circular cone is 5282 CM square if the diameter of its base is 16 then find its slant height area of its total surface​

Answer 1

Answer:

TSA = 5482.9... Cm²

Slant height = $\frac{18487}{88}$

Explanation:

Given:

Curved Surface area of a right circular cone = 5282cm²

Diameter of base = 16cm

Radius = $\frac{diameter}{2}$= 8 cm

The curved surface of a right circular cone is given by: $\pi rl$

where $\pi = \frac{22}{7}$

r = 8 cm

l = ?

Substituting the above values, we get:

$\frac{22}{7} \times 8 \times l = 5282$

$\frac{176}{7} \times l = 5282$

$l=5282 \times \frac{7}{176}$

$l =\frac{36974}{176} = \frac{18487}{88}$ cm

The slant height is equal to $\frac{18487}{88}$cm

Now solving for total surface are which is equal to = $\pi rl+\pi r^{2}$

Solving: 5282 + $\frac{22}{7} \times 64$

= 5482.9... Cm²

The total surface area of the cone is equal to 5482.9... Cm²

Answer 2

GIVEN :-

◙ Curved Surface area of a right circular cone = 5282 cm²

◙ Diameter of its base = 16 cm

TO CALCULATE :-

The slant height(l) and the TSA of the right circular cone.

FORMULAE TO BE USED :-

CSA of a right circular cone = $\displaystyle{\sf{\pi rl}}$

TSA of a right circular cone = $\displaystyle{\sf{\pi r(r+l)}}$

SOLUTION :-

Radius(r) = 16/2 = 8 cm

A/q,

$\displaystyle{\sf{\pi rl=5282\ cm^2}}\\\\\displaystyle{\sf{\implies \frac{22}{7} \times 8 l=5282}}\\\\\displaystyle{\sf{\implies 176l=36974}}\\\\\displaystyle{\sf{\implies l=\frac{36974}{176} }}\\\\\boxed{\displaystyle{\sf{\implies l=210.07\ cm}}}$

So, the slant height = 210.07 cm.

Now,

$\displaystyle{\sf{TSA=\pi r(r+l)=\frac{22}{7}\times8(8+210.07) }}\\\\\displaystyle{\sf{\implies TSA=\frac{176}{7}\times218.07 }}\\\\\displaystyle{\sf{\implies TSA=\frac{38380.32}{7} }}\\\\\boxed{\displaystyle{\sf{\implies TSA=5482.9\ cm^2}}}$

So, the total surface area of the cone is equal to 5482.9 cm².