A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm. Calculate the radius of the base of the cone.

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Solution

Let radius of cylinder be $r_{C}$

radius of cone be $r_{c}$

volume of cylinder = π $r_{C}$ ² h

volume of cone = $\frac{1}{3} π (r_{c}$ ²h)

volume of cylinder = volume of cone
$π (r_{C}) ² h_{C}$ = $\frac{1}{3} π (r_{c}) ² (h_{c})$

$(r_{c})^{2} = \frac{π 8 \times 8 \times 2}{\frac{1}{3} π \times 6}$

$(r_{c})^{2} = \frac{8 \times 8 \times 2}{2}$ cm³ .

$r_{c}$ = 8

hence , the base radius of cone is = 8 cm .

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A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm. Calculate the radius of the base of the cone.

Let radius of cylinder be rC radius of cone be rc volume of cylinder = πrC² h volume of cone = 13π(rc²h) volume of cylinder = volume of cone π(rC)²hC = 13π(rc)²(hc) (rc)2=π8×8×213π×6 (rc)2=8×8×22 cm³ . rc = 8 hence , the base radius of cone is = 8 cm .