Question

the volume of right circular cone is 9856cm³.If the radius of base 14 cm.find the----->
1. height of cone
2.Slant height​

Answer 1

Given :-

The volume of right circular cone is 9856cm³.If the radius of base 14 cm.

Find out :-

1. Height of cone
2. Slant height

Solution :-

• Volume of right circular cone = 9856cm³
• Radius of base = 14 cm

As we know that

→ Volume of cone = ⅓ πr²h

Where,

• r = radius
• h = height

According to the given condition

→ Volume of cone = 9856cm³

→ ⅓ πr²h = 9856

→ ⅓ × 22/7 × 14 × 14 × h = 9856

→ ⅓ × 22 × 2 × 14 × h = 9856

→ 44 × 14h/3 = 9856

→ h = 3 × 9856/44 × 14

→ l = 3 × 224/14

→ l = 3 × 16

→ l = 48 cm

•°• Height of cone = 48 cm

Now,

→ (Slant height)² = (radius)² + (height)²

→ l = √r² + h²

→ l = √(14)² + (48)²

→ l = √196 + 2304

→ l = √2500

→ l = 50 cm

•°• Slant height of cone is 50cm

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Answer 2

$\underline{\underline{\sf{\maltese\:\:Question}}}$

The volume of right circular cone is 9856 cm³. If the radius of base 14 cm. Find the :

• Height of Cone
• Slant Height

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• The volume of right circular cone = 9856 cm³

• Radius of Base = 14 cm

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• Height of Cone
• Slant Height

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• Height of Cone = 48 cm

• Slant Height of Cone = 50 cm

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

♣ First Let's Find Height of Cone

Volume of Right Circular Cone = 9856 cm³

⇒ 1/3πr²h = 9856 cm³

⇒ 1/3 × π × r² × h = 9856 cm³

⇒ 1/3 × 22/7 × r² × h = 9856 cm³   (∵ π = 22/7)

⇒ 22 × 1/7 × 3 × r² × h = 9856 cm³

⇒ 22/21 × r² × h = 9856 cm³

⇒ 22/21 × r² × h = 9856 cm³    (Given r = 14 cm)

⇒ 22/21 × (14 cm)² × h = 9856 cm³  

⇒ 22/21 × 196 cm² × h = 9856 cm³  

⇒ (22 × 196)/21  cm² × h = 9856 cm³  

⇒ 4312/21  cm² × h = 9856 cm³  

⇒ 616/3  cm² × h = 9856 cm³  

Multiplying both sides by 3

⇒ 3 × (616/3)  cm² × h = 3 × 9856 cm³  

⇒ 616 cm² × h = 29568 cm³  

Dividing both sides by 616 cm²

⇒ (616 cm² × h)/616 cm² = 29568 cm³/616 cm²

⇒ h = 29568/616 cm

⇒ h = 48 cm

∴ Height of Cone = 48 cm

_____________________________________________

♣ Now Let's Find Slant Height

Slant Height = √(r² + h²)

⇒ Slant Height = √[(14 cm)² + h²]  (Given r = 14 cm)

⇒ Slant Height = √[196 cm² + h²]  

⇒ Slant Height = √[196 cm² + (48 cm)²]  (We found : h = 48 cm)

⇒ Slant Height = √[196 cm² + 2304 cm²]

⇒ Slant Height = √[2500 cm²]

⇒ Slant Height = √[50² cm²]

⇒ Slant Height = √[50²] cm

⇒ Slant Height = 50 cm

∴ Slant Height of Cone = 50 cm

_____________________________________________

$\underline{\underline{\sf{\maltese\:\:Diagram}}}$

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf{14\:cm}}\put(9.5,10){\sf{48\:cm}}\end{picture}$

Know More :

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surfacearea formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

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