Question

a cone of height 12 CM has a volume 616 CM square then its diameter is how much centimetre​

Answer 1

Given :

• Height of cone = 12cm
• Volume of cone = 616cm³

To find :

Diameter of cone in cm

Formula used :

• Volume of cone = (1/3)πr²h
• Diameter = 2r

Solution :

$\sf Volume \: = \: \dfrac{1}{3} \pi \: {r}^{2} h \\ \\ \sf \implies \: \: 616\: {cm}^{3} = \: \frac{1}{3} \times \pi \times {r}^{2} \times 12cm \\ \\ \sf \implies \: {r}^{2} \: = \: \dfrac{616 \times 3\: cm^{3} }{ 12 \times \pi \: cm} \\ \\ \sf \implies \: {r}^{2} \: = \: \dfrac{616 \ {cm}^{2} }{4 \times \frac{22}{7} } \\ \\ \sf \implies \: {r}^{2} \: = \: \dfrac{154 \times 7 \: {cm}^{2} }{22} \\ \\ \sf \implies \: {r}^{2} \: = \: 7 \times 7 \: {cm \:}^{2} \\ \\ \sf \implies \: {r}\: = \sqrt{(7 \times 7 {cm}^{2} )} \\ \\ \sf \implies \: {r} = \: 7cm$

Therefore, diameter = 2r

Diameter = 2(7cm)

Diameter = 14 cm

ANSWER : 14cm