Question

the volume of cone is 1005 5/7cu.cm. the area of its base is 201 1/7sq.cm. find the slant height of the cone
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Answer 1

The slant height of the cone is 17 cm.

Step-by-step explanation:

• We are given the volume of a cone = $1005\dfrac{5}{7} \ cm^3$

• Also, we have the base area of this cone =  $201\dfrac{1}{7} \ cm^2$

• We are asked to find out the slant height of this cone.

We know that;

• The base of cone is a circle.

• So, base area = $\pi r^2$

$201\dfrac{1}{7} \ = \pi r^2$

$\dfrac{1408}{7} \ = \dfrac{22}{7} r^2$

$r^2 = 64$

$r = \pm8$

• Since, radius is a length. It can't be negative.

So,        r = 8 cm

• Now, Vol of cone = $1005\dfrac{5}{7} \ cm^3$

       $\dfrac{1}{3} \pi r^2 h = \dfrac{7040}{7}$

       $\dfrac{1}{3} \times \dfrac{22}{7} \times 8^2 h = \dfrac{7040}{7}$

By solving it, we get.

                          h = 15 cm

This is the height of cone.

Now, we can find out the slant height as;

• $(slant \ height)^2 = height^2 + r^2$ (refer the figure)

• Because, $\Delta ABC$ is a right angle triangle.

$(slant \ height)^2 = 15^2 + 8^2$

By solving the above expression, we get.

• Slant height = 17 cm

Thus, the slant height of the cone is 17 cm.