Question

6. The radius of a cone is 10 cm and the total the surface area of a cone is 880 cm². Find the slant height.​

Answer 1

❉Given:-

• Radius of cone = 10cm
• Total Surface area of cone = 880cm²

❂To Find:-

• Height of cone.

❃Required Response:-

$\boxed{\sf{Total\; Surface\;Area_{[Cone]} = {\pi}rh+\pi{r}^{2}}}$

Let, The Required Height be x

$880 = \frac{22}{7} \times10 \times x + \frac{22}{7} \times { (10) }^{2} \\ 880 = (\frac{220}{7})x + \frac{22}{7} \times 100 \\ 880 = ( \frac{220}{7} )x + (\frac{2200}{7} ) \\ 880 = \frac{220x + 2200}{7} \\ 880 \times 7 = 220x + 2200 \\ 6160 - 2200 = 220x \\ \cancel{\frac{3960}{220}} = x \\ x = 18$

Height of Cone

• $\longmapsto\;\red{\bold{18cm}}$

$\tt{@MrMonarque}$

Hope It Helps You ✌️

Answer 2

Given :

Radius , r = 10 cm.

Total surface area , A= 880 cm²

We have to find slant height l.

Also, TSA= πr(l+r)

Putting value of area and radius in above equation.

We get ,

800= 3.14×10×(l+10)

Solving above equation We get,

• L= 18.025cm

Hence , this is the required solution.