Question

The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface

A) 40pi sq.m B) 50pi sq.m C) 60pi sq.m D) 70pi sq.m

Answer 1

$\underline\mathbf{\star \: ANSWER \: \star}$

• C) 60π m² (✔)

GIVEN:

• Slant height of the cone (l) = 10 m
• Height of the cone (h) = 8 m

TO FIND:

• What is the C.S.A. of the cone ?

SOLUTION:

Let the radius of the cone be 'r' m

To find the radius, we use Pythagoras theorem

$\bf{\star \: (Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2\: \star}$

According to question:-

• Hypotenuse = 10 m
• Perpendicular = 8 m
• Base = r m

$\rm{\dashrightarrow (10)^2 = (8)^2 + (r)^2 }$

$\rm{\dashrightarrow 100 = 64 + r^2 }$

$\rm{\dashrightarrow 100 - 64 = r^2 }$

$\rm{\dashrightarrow 36 = r^2}$

$\rm{\dashrightarrow \sqrt{36} = r }$

$\bf{\dashrightarrow 6 \: m = r}$

To find the Curved surface area of the cone, we use the formula:-

$\large\bf{\star \: C.S.A. = \pi r l \: \star}$

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow C.S.A. = \pi \times 6 \times 10 }$

$\bf{\dashrightarrow \star \: C.S.A. = 60 \pi \: m^2 \: \star }$

❝ Hence, the C.S.A. of cone is 60π m² ❞

______________________

Answer 2

60pi sq mi.

Step-by-step explanation:

L= 10m H=8m

(H)sq. + (R)sq. = (L)sq.

(8m)sq + (R)sq. = (10m)sq.

(R)sq. = 100m sq. – 64m sq.

= 36m sq.

R sq. = √36m sq.

= 6 m

curved surface area = πrl

=π×6m×10m

60pi sq mi.