Question

A cone of radius 3cm has a curved surface area of 47.1cm² find the volume of cone (π=3.14 )
a 37.50cm³
b 68cm³
c 37cm²
d37.68cm³​

Answer 1

Answer :

›»› The volume of curved surface area of cone is 37.68 cm³.

Step-by-step explanation :

Given :

• Radius of cone = 3 cm.
• Curved surface area of cone = 47.1 cm².

To Find :

• Volume of cone = ?

How to find?

Here in this question we have to find the volume of cone, So, firstly we need to find the slant height of cone, after that we will find the height of cone, after all this we will find the volume of cone.

To find the slant of cone we use the formula of curved surface area of cone.

To find the height of cone we use the formula for finding the value of height.

To find the volume of cone we use the formula for finding the value of volume of cone.

Formula required :

Formula to calculate the slant height of cone is given by,

→ CSA = πrl.

Formula to calculate the height of cone is given by,

→ h² = l² - r².

Formula to calculate the volume of cone is given by,

→ Volume of cone = 1/3 πr²h.

Solution :

Firstly we will find the slant height of cone.

As we know that

→ CSA of cone = πrl

→ 47.1 = 3.14 * 3 * l

→ 47.1 = 9.42 * l

→ 47.1 = 9.42l

→ l = 47.1/9.42

→ l = 47100/9420

→ l = 4710/942

→ l = 5

The slant height of cone is 5 cm.

Now, we will find height of cone.

As we know that

→ h² = l² - r²

→ h² = (5)² - (3)²

→ h² = 25 - (3)²

→ h² = 25 - 9

→ h² = 16

→ h = √16

→ h = 4

The height of cone is 4 cm.

Now,

As we know that

→ Volume of cone = 1/3 πr²h

→ Volume of cone = 1/3 * 3.14 * (3)² * 4

→ Volume of cone = 1/3 * 3.14 * 9 * 4

→ Volume of cone = 1/3 * 3.14 * 36

→ Volume of cone = 1 * 3.14 * 12

→ Volume of cone = 3.14 * 12

→ Volume of cone = 37.68

Hence, the volume of cone is 37.68 cm³.

So, option (d) 37.68 cm³ is correct ✔.

Answer 2

${\bold{\sf{\underline{Understanding \: the \: question}}}}$

❖ This question says that there is a cone of radius 3 cm has a curved suface area of 47.1 cm² Afterthat this question ask us to find the volume of cone. There is a hint given for us and we have to use this hint to solve this question ; it's the value of π is 3.14 There are some options given these are given below ↧

Option a 37.50cm³

Option b 68cm³

Option c 37cm³

Option d 37.68cm³

${\bold{\sf{\underline{Given \: that}}}}$

❖ Radius of cone = 3 cm

❖ Curved surface area = 47.1 cm²

${\bold{\sf{\underline{To \: find}}}}$

❖ Volume of cone.

${\bold{\sf{\underline{Solution}}}}$

❖ Volume of cone = Option d 37.68cm³

${\bold{\sf{\underline{Using \: concepts}}}}$

❖ Volume of cone formula.

❖ Height of the cone formula.

❖ Slant height of cone formula.

${\bold{\sf{\underline{Using \: formula}}}}$

❖ Volume of cone = ⅓πr²h

❖ Height of the cone = h² = l² - r²

❖ Slant height of cone = C.S.A = πrl

${\bold{\sf{\underline{We \: also \: write \: these \: as}}}}$

❖ Length as l

❖ Breadth as b

❖ Height as h

❖ Curved surface area as C.S.A

❖ Radius as r

${\bold{\sf{\underline{Procedure \: of \: question}}}}$

❖ To solve this problem 1stly we have to find the slant height of cone and we have to use this formula ↦ C.S.A of cone = πrl. Afterwards putting the values we get slant height. Now we have to find the height of cone and we have to use this formula ↦ h² = l² - r² Now putting the values we get height of the cone. Now we have to find the volume of cone and we have to use this formula ↦ ⅓πr²h Now putting the values we get our final result means volume of given cone as 37.68cm³

${\bold{\sf{\underline{Full \: solution}}}}$

✠ Finding slant height of cone !

↦ C.S.A of cone = πrl

↦ 47.1 = 3.14 × 3 × l

↦ 47.1 = 9.42 × l

↦ 4.71 / 9.42 = l

↦ 47100 / 9420 = l

↦ 4710 / 942 = l

↦ 5 = l

↦ l = 5 cm

${\bold{\bf{\boxed{Hence \: slant \: height \: is \: 5 \: cm}}}}$

✠ Finding height of cone !

↦ h² = l² - r²

↦ h² = 5² - 3²

↦ h² = 25 - 9

↦ h² = 16

↦ h = √16

↦ h = 4 cm

${\bold{\bf{\boxed{Hence \: height \: is \: 4 \: cm}}}}$

✠ Finding volume of cone !

↦ Volume of cone = ⅓πr²h

↦ Volume of cone = ⅓ × 13.4 × 3² × 4

↦ Volume of cone = ⅓ × 13.4 × 9 × 4

↦ Volume of cone = ⅓ × 13.4 × 36

↦ Volume of cone = 1 × 13.4 × 12

↦ Volume of cone = 13.4 × 12

↦ Volume of cone = 37.68cm³

${\bold{\bf{\boxed{Hence \: volume \: is \: 37.68 cm^{3}}}}}$