Cone is an object which is hollow, but tapers down to a point at the other end known as the vertex.

A Cone is generated by rotating a right triangle in a clock wise direction or anticlockwise direction.

A Right circular cone is again generated by rotating a right angled triangle rotating clockwise or a clockwise.

Area of cone has the following specifications

Surface Area of cone = π b l where l^{2} = b^{2} + h^{2}

There are three formulas related to cone

1. Surface area of cone = π b l where b is the radius and l is the slant height.

2. Volume of cone = $\frac{1}{3}$ π b^{2} h. where h is the height of the cone.

3. Base area of cone = π b^{2}.

Volume of cone = $\frac{1}{3}$ π b^{2} h. where h is the height of the cone.

**1. Find the surface Area of the cone whose base radius is 3cm and height is 4 cm.**

**Answer:** Surface area of cone is given by π b l where b is base radius and l is the slant height.

l^{2} = b^{2} + h^{2}

= 3^{2} + 4^{2}

= 9+16

= 25

l = √25

l=5 cm

Surface Area of the cone = π b l = $\frac{22}{7}$ $\times 3 \times 5$

= 47.14 sq.cm.

**2. Find the surface Area of the cone whose base radius is 5cm and height is 12cm.**

**Answer:** Surface area of cone is given by π b l where b is base radius and l is the slant height.

l^{2} = b^{2} + h^{2}

= 5^{2} + 12^{2}

= 25+144

= 169

l = √169

l=13cm

Surface Area of the cone = π b l = $\frac{22}{7}$ $\times 5 \times 13$

= 204.28 sqcm.

**3. Find the volume of the cone whose base radius is 6 cm and height is 12 cm.**

**Answer:** The volume of the cone is given by $\frac{1}{3}$ π b^{2} h.

$\frac{1}{3}$ $\times$ $\frac{22}{7}$ $\times$ 6^{2} $\times$ 12 = $\frac{9504}{21}$

= 452.57 cubic cm.

**4. Find the volume of the cone whose base radius is 2 cm and height is 21 cm.**

**Answer:** The volume of the cone is given by $\frac{1}{3}$ π b^{2} h.

$\frac{1}{3}$ $\times$ $\frac{22}{7}$ $\times$ 2^{2} $\times$ 21 = $\frac{1848}{21}$

= 616 cubic cm

**5. Find the volume of the cone whose base radius is 4cm and height is 35 cm.**

**Answer:** The volume of the cone is given by $\frac{1}{3}$ π b^{2} h.

$\frac{1}{3}$ $\times$ $\frac{22}{7}$ $\times$ 4^{2} $\times$ 35 = $\frac{1760}{7}$

= 251.42cubic cm.

**6. Find the surface Area of the cone whose base radius is 5cm and height is 6cm.**

**Answer:** Surface area of cone is given by π b l where b is base radius and l is the slant height.

l^{2} = b^{2} + h^{2}

= 5^{2} + 6^{2}

=25+36

= 71

l = √71

l=8.42cm

Surface Area of the cone = π b l = $\frac{22}{7}$ $\times 3 \times$ 8.42

= 79.44 square cm.

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