Question

If upper and lower radii of a frustum are 5cm and 1 cm respectively and the distance between them is 3cm then the slant height is

Answer 1

✬ Slant height = 5 cm ✬

Step-by-step explanation:

Given:

• Upper and lower radii of a frustum are 5 & 1 cm.
• Distance between them i.e height of frustum is 3 cm.

To Find:

• What is the slant height ?

Solution: Let upper radii be R = 5 cm & lower radii be 1 cm.

As we know that :-

★ Slant Height of frustum = Slant height of the cone = √ (R – r)² + h² ★

$\implies{\rm }$ L = √ (5 – 1)² + 3²

$\implies{\rm }$ L = √4² + 3²

$\implies{\rm }$ L = √4 $\times$ 4 + 3 $\times$ 3

$\implies{\rm }$ L = √16 + 9

$\implies{\rm }$ L = √25

$\implies{\rm }$ L = 5 cm

Hence, the slant height of the frustum is 5 cm.

Answer 2

GIVEN:

• Upper radius of the frustum = 5 cm
• Lower radius of the frustum = 1 cm
• Height of the frustum = 3 cm

TO FIND:

• What is the slant height (l) of the frustum ?

SOLUTION:

Let the upper radius of the frustum be 'R' and lower radius of the frustum be 'r'

We know that the formula for finding the Slant height (l) of the frustum is:-

$\large\bf{\star \: l = \sqrt{(R-r)^2 + h^2} \: \star }$

According to question:-

On putting the values in the formula we get

$\rm{\dashrightarrow l = \sqrt{(5-1)^2 + 3^2}}$

$\rm{\dashrightarrow l = \sqrt{4^2 + 3^2}}$

$\rm{\dashrightarrow l = \sqrt{16 + 9}}$

$\rm{\dashrightarrow l = \sqrt{25}}$

$\large\bf{\dashrightarrow \star \: l = 5 \: cm \: \star}$

❝ Hence, the slant height (l) of the frustum is 5 cm ❞

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