Question

The volume of a right circular cone is 28cm find height of the cone
​

Answer 1

Correct Question :-

• The volume of a right circular cone is 9856cm³ . If the diameter of the base is 28cm , then find height of the cone

Given :-

• Volume of Cone = 9856cm³
• Diameter of the Cone = 28cm

To Find :-

• Height of the Cone .

Solution :-

★ Radius of the Cone ★

${:} \longrightarrow \sf{\sf{Radius \: of \: the\: Cone \: = \: \dfrac{Diameter}{2} }}\\ \\ {:} \longrightarrow \sf \: Radius \: of \: the\: Cone \: = \: \dfrac{28}{2} \\ \\ {:} \longrightarrow \bf \: radius \: of \: the\: Cone \: = \: 14cm$

━━━━━━━━━━

★ Height of the Cone ★

$\longmapsto \sf{\sf{Volume \: of \: the\: Cone \: = \: \dfrac{1}{3} \: \times \: \pi\: (Radius)^{2} \: \times \: Height }}\\ \\ \longmapsto \sf \: 9856 \: = \: \dfrac{1}{3} \: \times \: \dfrac{22}{7} \: \times \: (14)^{2} \: \times \: Height\\ \\ \longmapsto \sf \: 9856\: = \: \dfrac{1}{3} \: \times \: \dfrac{22}{ \cancel7} \: \times \: \cancel{14} \: \times \: 14 \: \times \: Height \\ \\ \longmapsto \sf 9856\: = \: \dfrac{1}{3} \: \times \: 22 \: \times \: 2 \: \times \: 14 \: \times \: Height \\ \\ \longmapsto \sf 9856\: = \: \dfrac{616}{3} \: \times \: Height \\ \\ \longmapsto \sf \dfrac{9856 \: \times 3}{616}\: = \: Height \\ \\ \longmapsto \sf \cancel\dfrac{29568}{616}\: = \: Height \\ \\ \longmapsto \bf 48\: = \: Height$

━━━━━━━━━━

So, Height of The Cone is 48cm

━━━━━━━━━━

Formulas Related to Cone :-

• Volume of cone = ⅓ πr²h
• C.S.A of cone = πrl
• T.S.A of cone = πrl + πr²

━━━━━━━━━━

Answer 2

Step-by-step explanation:

⠀━━━━━━━━━━━━━━━━━━━━━━━━

$\huge\pink{\mid{\fbox{\tt{QųEsTɪOη}}\mid}}$

The volume of a right circular cone is 28cm find height of the cone

⠀━━━━━━━━━━━━━━━━━━━━━━━━

$\huge{\underline{\mathrm{Given\: :}}}$

$\sf\blue{r = \frac{28}{2 } = 14cm }$

∴ Let the height be = h

$\sf\red{⇒Volume =28cm = \frac{1}{3} \pi \: {r}^{2} h }$

$\sf\red{⇒ 28= \frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times h }$

${\boxed{h = 48cm }}$

⠀━━━━━━━━━━━━━━━━━━━━━━━━

∴ Therefore, The height of the cone is 48cm.