Question

the height of a cone is 15 CM if its volume is 1004.8 cm cube find the radius of base use pi as 3.14​

Answer 1

★ Answer :-

• The radius = 8 cm

★ GivEn :-

• The height of the cone is 15 cm.
• The volume of the cone is 1004.8 cm^3

★ To Find :-

• The radius of the base of the cone.

★ Diagram :-

$\setlength{\unitlength}{30} \begin{picture}(10,6) \linethickness{1.2} \qbezier(1,1)(3., 0)(5,1)\qbezier(1,1)(3.,2)(5,1)\put(3,1){\circle*{0.15}}\put(3,1){\line(0,1){3}}\qbezier(1,1)(1,1)(3,4)\qbezier(5,1)(3,4)(3,4)\put(3,1){\line(1,0){2}}\put(3.2,1.1){ \bf r \: cm }\put(1.9,1.9){ \bf 15 \: cm }\put(4,3.5){\boxed{ \bf @TheFairyTale }}\end{picture}$

★ Solution :-

Let the radius of the base be r cm.

We know, the volume of cone is

$\implies \underline{\boxed { \red{\sf \: V_{cone} = \dfrac{1}{3} \times \pi \: {r}^{2} h}}}$

Now, putting the values we get,

$\implies \sf \: 1004.8 = \dfrac{1}{3} \times 3.14 \times {r}^{2} \times 15$

$\implies \sf \: 1004.8 = 3.14 \times {r}^{2} \times 5$

$\implies \sf \: 1004.8 = 15.7 \times {r}^{2}$

$\implies \sf \: {r}^{2} = \dfrac{1004.8}{15.7}$

$\implies \sf \: {r}^{2} = 64$

$\implies \underline{\boxed { \red{\sf \: r = \sqrt{64} = 8 }}}$

Therefore, the radius of base of the cone is 8 cm