Question

a frustum of a right circular cone which is of height 8 cm with radii of its circular ends as 10 cm and 4cm has its slant height equal to​

Answer 1

Answer:

the answer

of this question is given above

Answer 2

To Find :-

The slant height of the Frustum.

Given :-

• Height of the Frustum = 8 cm

• Outer Radius = 10 cm

• Inner Radius = 4 cm

We know :-

⠀⠀⠀⠀⠀⠀Slant height of a Frustum :

$\boxed{\underline{\bf{l = \sqrt{(R - r)^{2} + h^{2}}}}}$

Where :-

• R = Outer Radius of the Frustum
• r = Inner Radius of the Frustum
• h = Height of the Frustum
• l = Slant height of the Frustum

Solution :-

Given :-

• R = 10 cm

• r = 4 cm

• h = 8 cm

Using the formula and substituting the values in it, we get :-

$:\implies \bf{l = \sqrt{(R - r)^{2} + h^{2}}} \\ \\ \\ :\implies \bf{l = \sqrt{(10 - 4)^{2} + 8^{2}}} \\ \\ \\ :\implies \bf{l = \sqrt{6^{2} + 8^{2}}} \\ \\ \\ :\implies \bf{l = \sqrt{36 + 64}} \\ \\ \\ :\implies \bf{l = \sqrt{100}} \\ \\ \\ :\implies \bf{l = 10} \\ \\ \\ \therefore \purple{\bf{l = 10 cm}}$

Hence, the slant height of the Frustum is 10 cm.