Question

If volume of a cone is 132cm cube and height of cone is 14 cm .then find slant height of cone

Answer 1

Answer:

$\sf volume \: of \: cone \: is \: \: \: \pi {r}^{2} \frac{h}{3 } \\ \\ \sf volume \: is \: give \: = 132cm \\ \sf height = 14cm \\ \\ \sf 132 = \pi {r}^{2} \frac{14}{3} \\ \sf 132 = \frac{22}{7} \times {r}^{2} \times \frac{14}{3} \\ \sf 132 = \frac{44 \times {r}^{2} }{3} \\ \sf 132 \times 3 = 44 \times {r}^{2} \\ \sf 396 = 44 {r}^{2} \\ \sf {r }^{2} = \frac{396}{44} \\ \sf {r }^{2} = 9 \\ \sf r = 3 \\ \\ \sf to \: find \: the \: slant \: hight \\ \sf r = 3 \\ \sf h = 14 \\ \sf use \: pythagoras \: theorm \\ \sf let \: slant \: \sf height = x \\ \sf {x}^{2} = {h}^{2} + {r}^{2} \\ \sf {x}^{2} = {(14)}^{2} + {(3)}^{2} \\ \sf{x}^{2} = 196 + 9 \\ \sf {x}^{2} = 205 \\ \sf x = \sqrt{205} \\ \\ \sf slant \: height \: = \sqrt{205}$

Answer 2

Given :-

ㅤㅤㅤㅤ• Volume of a cone is 132 cm!

ㅤㅤㅤㅤ• Height of cone is 14 cm!

To Find :-

ㅤㅤㅤㅤ• Slant height of cone?

❂ How to solve it :-

Here, we have height and volume of a cone, we had to find out it's slant height. Firstly we will find it's radius by using formula of volume of cone i.e (⅓ πr²h). By putting all values, we get it's radius and then we will use formula of slant height i.e l² = r² + h².

❂ So, let's start solving :-

Using formula of volume of cone :-

★ [ Volume of cone = ⅓ πr²h ] ★

Putting all values :-

➱ㅤㅤㅤ132 = 1/3 × 22/7 × r² × 14

➱ㅤㅤㅤ132 = 14/3 × 22/7 × r²

➱ㅤㅤㅤ(132 × 3 × 7)/14 × 22 = r²

➱ㅤㅤㅤ(132 × 3)/2 × 22 = r²

➱ㅤㅤㅤ396/44 = r²

➱ㅤㅤㅤ9 = r²

➱ㅤㅤㅤr = √9

➱ㅤㅤㅤr = √(3 × 3)

➱ㅤㅤㅤ[ r = 3 ] ★

∴ Radius of cone = 3 cm

Now, finding it's slant height :-

Formula :- ★ [ l² = r² + h² ] ★

Putting all values :-

➱ㅤㅤㅤl² = (3)² + (14)²

➱ㅤㅤㅤl² = 9 + 196

➱ㅤㅤㅤl² = 205

➱ㅤㅤㅤ[ l = √205 ] ★

∴ Slant height of cone is √205

Note :-

[ For diagram refer the attachment! ]