Question

If the volume of a right circular cone of height 9 cm is 48 te cm”, find the diameter of its
base.​

Answer 1

Correct Question:

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If the volume of a right circular cone of height 9 cm is 48 $\pi$ cm$^{3}$ , find the diameter of its base.

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Given:

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• Height of right circular cone is 9 cm
• Volume of the right circular cone is 48
• $\pi$ cm$^{3}$

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To find:

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Diameter of its base

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Solution:

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Let the radius of the base of the right circular cone be r cm.

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We know that,

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Volume of right circular cone

= 1/3 $\pi$ r$^{2}$ h

$\implies$ 1/3 $\pi$ r$^{2}$ h = 48 $\pi$

$\implies$ 1/3 r$^{2}$ h = 48

$\implies$ 1/3 × r$^{2}$ × 9 = 48

$\implies \: r {}^{2} = \frac{48 \times 3}{9} \\ \\ \implies \: r {}^{2} = 16 \\ \\ \implies \: r = 4 \: \: cm$

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Now we know that diameter = 2r

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So, diameter of its base = 2 × 4 = 8 cm.

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Hence, 8 cm is the solution.

Answer 2

Correct Question:

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If the volume of a right circular cone of height 9 cm is 48π cm³ , then find the diameter of its base.

Given:

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Height = 9 cm

Volume of cone = 48πcm³

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To find:

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What's the diameter of its base ?

Solution:

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So, we consider the radius of base of the right circular cone be r cm.

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Now , applying the formula of volume of cone

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Volume of cone :-

= 1/3πr²h

1/3 $\pi$ r$^{2}$ h = 48 $\pi$

1/3 r$^{2}$ h = 48

1/3 × r$^{2}$ × 9 = 48

r² = 48 × 3 / 9

r² = 16

r = √16

Radius = 4 cm

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Hence ,

Now ,

Diameter = 2r = 2 × 4 = 8 cm .

Additional Information :-

❥ Perimeter of Rectangle = 2( L + B )

❥ Perimeter of square = 4 × Side

❥ Perimeter of triangle = AB + BC + CA

❥ Area of Rectangle = L × B

❥ Area of Square = ( side ) ²

❥ Area of Rhombus = Product of Diagonal/2.

❥ Area of Parallelogram = Base × Height.

❥ Area of triangle = 1/2 × base × height .