Question

the area of the base of a right circular cone is 346.5cm square and the height of the cone is 27 cm. find it's volume of cone



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Answer 1

Given :-

• Area of the base of a right circular cone is 346.5 cm².
• Height of the cone is 27 cm.

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To find :-

• Volume of the cone.

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Solution :-

• We have area of base and height of a right circular cone.

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As we can see that, formula of Volume of a cone can be written as

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★ Volume = ⅓πr²h

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By dividing this formula into two parts, we can write

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★ Volume = πr² × h/3

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In this question we have area of base i.e., πr² and height (h).

Therefore,

• πr² = 346.5
• h = 27

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❏ Putting the values in the formula.

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→ Volume = 346.5 × 27/3

→ Volume = 346.5 × 9

→ Volume = 3,118.5 cm³

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Hence,

• Volume of the cone is 3,118.5 cm³.

Answer 2

Given :-

• Area of the base of right circular cone = 346.5 cm²
• Height of that cone = 27 cm

To Find :-

• Volume of that  cone

Solution :-

→ Base of a cone is circular so ,

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

$\star\: \boxed{\sf{\blue{Area\;of\;base\;of\;cone = \pi r^{2}}}}$

→ Let's put the values in the formula

$\sf \implies \pi r^{2} = 346.5$

$\sf \implies r^{2} = \dfrac{346.5}{\pi }$

→ ATQ we need to find the volume of that right circular cone

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

$\star\: \boxed{\sf{\blue{Volume\;=\dfrac{1}{3}\pi r^{2}h }}}$

→ Let's put the values in the formula in order to find the volume .  

$\sf \implies \dfrac{1}{3} \times \dfrac{22}{7} \times \dfrac{346.5}{\pi } \times 27$

$\sf \implies \dfrac{1}{3} \times \dfrac{22}{7} \times 346.5 \times \dfrac{7}{22} \times 27$

$\sf \implies \dfrac{1}{3} \times 346.5 \times 27$

$\sf \implies 346.5 \times 9$

$\sf \implies 3118.5 \; cm^{3}$

∴ Volume of the right circular cone is 3118.5 cm³

More about Cone :-

★ Curved Surface area of cone = πrl

★ Total Surface area of cone = πr( l + r )

★ Slant height of cone ( l ) = √h² + r²