Question

If radius and height of cone are 6 cm and 7 cm respectively then the volume of the cone is [ ]
(A) 264 cm3 (B) 154 cm3 (C) 164 cm3 (D) 254 cm3

Answer 1

Answer:

Explanation:

Given :

• Radius of a cone (r) = 6 cm
• Height of a cone (h) = 7 cm

To Find :

• The volume of a cone.

Formula to be used,

• Volume of cone = 1/3 × πr^2h

Solution,

★Volume of cone,

1/3 × πr^2h

⇒ 1/3 × 22/7 × (6)^2 × 7

⇒ 1/3 × 22 × 36

⇒ 22 × 12

⇒ 264 cm^3

Hence, The volume of a cone is 264 cm^3.

Answer 2

Answer:

option a is correct

Step-by-step explanation:

Diagram:-

$\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(18,1.6){\sf {6\:cm} }\put(9.5,10){\sf {7\:cm} }\end{picture}$

Given:-

In a cone

• Radius =r=6cm
• Height=h=7cm

To find:-

Volume of the cone

Solution:-

As we know that in a cone

$\boxed{\sf Volume=\dfrac {1}{3}\pi r^2h }$

• Substitute the values

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow Volume=\dfrac {1}{3}\times \dfrac {22}{\cancel {7}}\times (6)^2\times \cancel {7}$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow Volume =\dfrac {22}{3}\times 36$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow Volume =\dfrac {22\times \cancel {36}}{\cancel {3}}$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow Volume =22\times 12$

$\\\qquad\quad\displaystyle\sf {:}\longrightarrow Volume =264cm^3$

$\\\\\therefore\sf Volume\:of\:the\:cone\:is\:264cm^3$

Formulas related to cone:-

$\sf \star\:Area\:of\:Base =\pi r^2 \\\\ \sf \star \:\:Curved \: Surface \: Area = \pi rl\\\\\sf\star \:\:TSA = Area\:of\:Base + CSA=\pi r^2+\pi rl\\ \\\star\sf \: \:Volume=\dfrac{1}{3}\pi r^2h\\ \\\star\sf \: \:Slant \: Height=\sqrt{r^2 + h^2}$