Question

The height of a right circular cone whose radius is 5 cm and slant height is

13 cm will be

a) 12 cm b) 10 cm c) 13 cm d) 5 cm​

Answer 1

Answer:

12

Step-by-step explanation:

Given:-

Slant height of the cone=13 cm

Radius=5 cm

To find:-

Height of the cone.

Solution:-

Slant height(13²)=$\sqrt{h^{2}+5^{2} }$

h²=$\sqrt{13^{2}-5^{2} }$

$\sqrt{13^{2}-5^{2} } \\=\sqrt{169-25} \\=\sqrt{144} \\=12^{2}$

Therefore, the correct a 12cm.

                                                           

Facts about right circular cone:-

• Volume =$\frac{1}{3}$πr²h

• Curved surface area of right circular cone = π r l

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(17,1.6){\sf{5cm}}\put(9.5,10){\sf{12cm}}\put(20,10){\sf{13cm}}\end{picture}$

Answer 2

Required Answer:

12

Step by step Explanation:

Given:-

Slant height of the cone=13 cm

Radius=5 cm

To find:-

Height of the cone.

Solution:

By,Pythagoras theorem:

H² = B² + P²

13² = 5² +P²

169 = 25 +P²

P² = 169-25

P² = 144

P = √144

P= 12cm

$\therefore \underline{\boxed{\textbf{\textsf{\pink{Height\: of\:right circular cone is = 12 cm}}}}}$

Note:

In Pythagoras theorem:

H = Hypotenuse (slant height)

B = Base (radius in this question)

P = Perpendicular (Height)

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(17,1.6){\sf{5cm}}\put(9.5,10){\sf{12cm}}\put(20,10){\sf{13cm}}\end{picture}$