Question

the curved surface of a right circular cone is 198 CM square and the radius of its base is 7 cm find the volume of the cone​

Answer 1

Given:-

• Curved surface Area of a right-circular cylinder = 198 cm²
• Radius of its base = 7 cm

To Find:-

Volume of the cone.

Solution:-

We know,

$\sf{CSA\:of\:a\:cylinder = 2\pi rh\:\:sq.units}$

Therefore,

$\sf{198 = 2\pi rh}$

= $\sf{\dfrac{198}{2} = \dfrac{22}{7} h}$

= $\sf{\dfrac{198\times 7}{2\times 22} = h}$

= $\sf{\dfrac{63}{2} = h}$

= $\sf{h = 31.5\:cm}$

Now,

We know,

$\sf{Volume\:of\:cylinder = \pi r^2h}$

= $\sf{Volume = \dfrac{22}{7} \times (7)^2 \times 31.5}$

= $\sf{Volume = \dfrac{22}{7}\times 7\times 7\times 31.5}$

= $\sf{Volume = 22\times 7\times 32.5}$

= $\sf{Volume = 4851\:\:cm^3}$

Therefore Volume of the cylinder is 4851 cm³

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Formulas to be kept in mind:-

• Volume of cylinder = πr²h cu.units
• Curved Surface Area (CSA) of cylinder = 2πrh sq.units
• Lateral Surface Area (LSA) of cylinder = 2πr(r+h) sq.units

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