Question

8. The diameter of base of a pyramid in the form of a right circular cone is 56
metre and the area of lateral surface is 3080 sq. metre. Find the height of the
pyramid​

Answer 1

Answer:

35 m

Step-by-step explanation:

Radius of the base R = 56/2 = 28 m

LSA = 3080

1/2 * perimeter of the base × h = 3080

1/2 * 2×22/7 ×28× h = 3080

h = 35 m

Answer 2

Answer :

Given :

• The diameter of base of a pyramid in the form of a right circular cone is 56m
• The area of lateral surface is 3080 m square.

Find :

• The height of the pyramid .

Solution :

We have,

• The diameter of the circular base = 56
• Then the radius is $\dfrac{56}{2}$ = 28

Now, what we have

• The radius of the base = 28 m
• The lateral surface of the cone = 3080 m square.

$\dag$ Formula to be used :

$\large{\boxed{\boxed{\rm{Lateral\: surface\: Cone=\dfrac{1}{2}×Circumference×height}}}}$

Putting values in formula :

$\dashrightarrow$ ${\rm{ Surface\: Area=\dfrac{1}{2}×Circle\:Circum×h}}$

$\dashrightarrow$ ${\rm{3080=\dfrac{1}{2}×2×\pi×r×height}}$

$\dashrightarrow$ ${\rm{3080=\dfrac{1}{2}×2×3.14×28×height}}$

$\dashrightarrow$ ${\rm{3080=2×3.14×14×height}}$

$\dashrightarrow$ ${\rm{3080=87.92×height}}$

$\dashrightarrow$ ${\rm{\dfrac{3080}{87.92}=height}}$

$\dashrightarrow$ ${\rm{35=height}}$

•°• The height of the cone is 35 m.

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