Question

Find the volume of a cone, the circumference of whose base is 88 cm and whose
height is 15.5 cm.​

Answer 1

$\huge{\green{\underline{\underline{\overline{\tt{\diamond\; Solution:}}}}}}$

Given,

Height of cone = 15.5cm

Circumference of base = 88cm

Let, Radius be 'r'

$☆\;{\boxed{\sf{Circumference\;of\;Cirlce = 2πr}}}$

$→\;\Large{\sf{2×\frac{22}{7}×r = 88}}$

$→\;\Large{\sf{r = \frac{88×7}{22×2}}}$

$→\;\Large{\sf{r = \cancel{\frac{616}{44}}}}$

$→\;{\sf{r = 14cm}}$

.:. Radius of base = 14cm.

$☆\;{\boxed{\sf{Volume\;of\;Cone = \frac{1}{3}πr²h}}}$

$→\;\Large{\sf{\frac{1}{3}×\frac{22}{7}×14×14×15.5}}$

$→\;\Large{\sf{\frac{22×14×14×15.5}{3×7}}}$

$→\;\Large{\sf{\frac{66,836}{21}}}$

$☞\;{\bf{3182.6cm³}}$

.:. Volume of Cone ◕➜ $\fbox\red{3182.6cm³}$

Hope It Helps You ✌️

Answer 2

Given :

• Base of the cone is 88 cm
• Height of the cone is 15.5 cm

To find :

• the volume and the circumference of the cone

Solution :

Let the radius be r

As we know,

$\huge\star{ \color{gold}{ \boxed{ \sf{ \color{cyan}{circumference \: of \: a \: circe = 2 \pi \: r}}}}}\star$

$\\ \tt \implies2 \times \frac{22}{7} \times r = 88$

$\\ \sf \implies \: r = \frac{ \cancel{88} \times 7}{ \cancel{22} \times \cancel2}$

$\\ \sf \implies \: r = 14$

Therefore, Radius of the triangle is 14 cm

As we know,

$\huge \star{ \color{red}{ \boxed{ \sf{ \color{purple}{{volume \: of \: a \: cone = \frac{1}{3} \pi \: r {}^{2} h}}}}}} \star$

$\\ \implies \sf \: \frac{1}{3} \times \frac{22}{7} \times {14}^{2} \times 15.5$

$\\ \implies \sf \frac{22 \times 14 \times \cancel{14} \times 15.5}{3 \times \cancel7}$

$\\ \implies \sf \frac{66836}{21}$

$\\ \implies \sf3182.66$

Therefore, Area of the cone is 3182.66 cm³