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Home » Find the curved surface area, the total surface area and the volume of a cone if its: iii. Height , diameteriv. Height , diameter
Find the curved surface area, the total surface area and the volume of a cone if its: iii. Height =16cm, diameter=24cmiv. Height =8cm, diameter =12cm
Class 10 | Frank | ICSE | Maths | Mensuration II
Find the curved surface area, the total surface area and the volume of a cone if its: iii. Height =16cm, diameter=24cmiv. Height =8cm, diameter =12cm

(iii)

Solution: –

According to the given question, we have the value of height and the diameter of the cone.

The height is 16 cm and the diameter is 24cm.

First, we should find the radius of the cone,

We know that, the radius is half the diameter.

r=\frac{d}{2}=\frac{24}{2}=12cm

We know that, the curved surface area is \left( \pi r\sqrt{\left( {{h}^{2}}+{{r}^{2}} \right)} \right)

=\left( \frac{22}{7} \right)\times 12\times \sqrt{\left( {{16}^{2}}+{{12}^{2}} \right)}

=\left( \frac{22}{7} \right)\times 12\times \sqrt{\left( 400 \right)}

=\left( \frac{22}{7} \right)\times 12\times 20

=754.29c{{m}^{2}}

Then, the total surface area =the area of circular base + curved surface area,=\pi {{r}^{2}}+\left( \pi r\sqrt{\left( {{h}^{2}}+{{r}^{2}} \right)} \right)

=\frac{22}{7}\times {{12}^{2}}+754.29

=452.57+754.29

=1206.86c{{m}^{2}}.

Therefore, the total surface area is 1206.86c {{m} ^ {2}}.

Now, we should find the value of the cone,

We know that, the volume of the cone is \frac{1}{3}\times \left( \pi {{r}^{2}} \right)\times h

=\frac{1}{3}\times \left( \left( \frac{22}{7} \right)\times {{12}^{2}} \right)\times 16 =2413.71c{{m}^{3}}

(iv)

Solution: –

According to the given question, we have the value of the height and the diameter of the cone.

The height is 8cm and the diameter is 12cm.

We know that, the radius is half of the diameter.

r=\frac{d}{2}=\frac{12}{2}=6cm

We know that, the curved surface area is \left( \pi r\sqrt{\left( {{h}^{2}}+{{r}^{2}} \right)} \right)

=\left( \frac{22}{7} \right)\times 6\times \sqrt{\left( {{8}^{2}}+{{6}^{2}} \right)}

=\left( \frac{22}{7} \right)\times 6\times \sqrt{100}

=\left( \frac{22}{7} \right)\times 6\times 10

=188.57c{{m}^{2}}

Then, the total surface area = the area of circular base + curved surface area.

=\pi {{r}^{2}}+\left( \pi r\sqrt{{{h}^{2}}+{{r}^{2}}} \right)

=\left( \frac{22}{7} \right)\times {{6}^{2}}+188.57

=113.14+188.57

=301.71c{{m}^{2}}

Therefore, the total surface area is 301.71c{{m}^{2}}

Now, we should find the volume of the cone.

We know that, the formula of the volume is \frac{1}{3}\times \left( \pi {{r}^{2}} \right)\times h.

=\frac{1}{3}\times \left( \left( \frac{22}{7} \right)\times {{6}^{2}} \right)\times 8

=301.71c{{m}^{3}}.

i

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