Question

The volume of a right circular cone is 176m3

. If the radius of the base is 7m then

find the height of the cone. Also find slant height. [ π =

22/

7

]​

Answer 1

Given :

• The volume of a right circular cone is 176m³. The radius of the base is 7m.

To Find :

• Height of the cone = ?
• Slant Height of the cone = ?

Solution :

⌖ Volume of right circular cone = 176 m³.

⌖ Radius of the base of cone = 7 m

⌖ Height of cone = ?

⌖ Slant Height of the cone = ?

❒ Finding height of the right circular cone :

→ Volume of cone = ⅓πr²h

→ 176 = ⅓πr²h

→ 176 = ⅓ × 22/7 × (7)² × h

→ 176 = ⅓ × 22 × 7 × h

→ 176 × 3 = 22 × 7 × h

→ 528 = 154 × h

→ h = 528 ÷ 154

→ h = 3.43 m

• Hence,the height of the right circular cone is 3.43 m.

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━

❒ Let's find the slant height of the right circular cone :

→ Slant Height = √(Height)² + (Radius)²

→ Slant Height = √(3.43)² + (7)²

→ Slant Height = √11.765 + 49

→ Slant Height = √60.765

→ Slant Height = 7.8 m

• Hence,the slant height of the right circular cone is 7.8 m.

═════════════════════════

Answer 2

$\huge{\boxed{\rm{Question}}}$

The volume of a right circular cone is 176m³. If the radius of the base is 7m then find the height of the cone. Also find slant height. [ π = 22/7 ]

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• The volume of a right circular cone is 176m³.

• The radius of the base is 7 m.

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• The height of the cone.

• Slant height.

• Value of π is 22/7

$\large{\boxed{\boxed{\sf{Solution}}}}$

• The height of the cone = 3.43 m

• Slant height = 7.8 m

$\large{\boxed{\boxed{\sf{Using \: formulas}}}}$

• Volume of cone = ⅓πr²h

• Slant height of cone = √(Height)² + (Radius)²

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that the volume of a right circular cone is 176m³ afterthat it says that if the radius of the base is 7m then it ask us to find the height of the cone and slant height of the cone also. It give us a hint also that value of π is 22/7.

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: problem}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question's first part that is to find the height of the cone we have to know the formula to find the volume of cone that is ready known to us . It's ⅓πr²h so according to this formula we have to put the values. After that we get the result of 1st part that is 3.43 metres. Afterthat we have to find the 2nd part of the question that is to find Slant height and again the formula is known by us. Its √(Height)² + (Radius)². Now putting the values according to this formula we get result of our 2nd part that is 7.8 metres. Hence the given question is solved !

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

According to the given question we know that what is given or what to find so let's see it again properly !!

• ( Given ) The radius of the base of a right circular cone is 7m.

• ( Given ) The volume of a right circular cone is 176m³.

• ( To find ) Height of the cone.

• ( To find ) Slant of the cone.

◌ Now we have to find the height of the cone ➝

□ To solve this part of question we have to know the the formula to find the volume of cone that is ⅓πr²h

■ Putting the values according to this formula we get the following results ➜

☛ Volume of cone = ⅓πr²h

☛ 176 = ⅓πr²h

☛ 176 = ⅓ × 22/7 × (7)² × h

☛ 176 = ⅓ × 22/7 × 7 × 7 × h

☛ 176 = ⅓ × 22 × 7 × h { We cut 7 by 7 here that's why we don't write then in this point }

☛ 176 × 3 = 22 × 7 × h

☛ 528 = 154 × h

☛ h = 528 / 154

☛ h = 3.43 m

Hence, ❛ 3.43 metres ❜ is the height of the right circular cone.

◌ Now we have to find the slant height of the cone ➝

□ To solve this part of question we have to know the the formula to find the slant height of the right circular cone is √(Height)² + (Radius)²

■ Putting the values according to this formula we get the following results ➜

☛ Slant height = √(3.43)² + (7)²

☛ Slant height = √11.765 + 49

☛ Slant height = √60.765

☛ Slant height = 7.8 m

Hence, ❛ 7.8 metres ❜ is the slant height of the right circular cone.