Question

The volume of a solid cone for which area of the base is 45 cm2 and height is 10cm is

Answer 1

Answer:

Volume = 142.88 cm³

Step-by-step explanation:

Given:

• Base area of cone = 45 cm²
• Height of cone = 10 cm

To find:

Volume of solid cone = ?

Solution:

The base of the cone is a circle.

Area of circle = πr²

⇒ 45 = 22/7 × r²

⇒ r² = (45 × 7) ÷ 22

⇒ r² = 14.31

⇒ r = √14.31

⇒ r = 3.78 cm

Now,

$\maltese\: \: \boxed{\red{\sf{Volume\:of\:cone=\dfrac{1}{3}\pi r^{2}h}}}$

where:

• r is the radius of the cone
• h is the height of the cone.

Substitute the given values in the above formula to find out the volume of cone.

$\hookrightarrow \: \sf{Volume\:of\:cone=\dfrac{1}{3} \times \dfrac{22}{7} \times (3.78)^{2}\times 10}$

$\dashrightarrow \: \: \sf{Volume\:of\:cone=\dfrac{22\times 3.78 \times 3.78 \times 10}{21}}$

$\therefore \boxed{\pink{\bf{Volume\:of\:solid\:cone=142.884 cm^{3}}}}$