Question

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of cone is equal to its radius. Find the volume of the solid in terms of pie.​

Answer 1

✬ Volume = π cm³ ✬

Step-by-step explanation:

Given:

• A solid is in shape of cone standing on a hemisphere.
• Radii of cone and hemisphere is equal to 1 cm.
• Height of cone is equal to its radius.

To Find:

• Volume of solid in terms of π.

Solution: Here in cone we have

• Radius = 1 cm
• Height = 1 cm

In hemisphere

• Radius = 1 cm

As we know that

★ Volume of Cone = 1/3πr²h ★

★ Volume of Hemisphere = 2/3πr³ ★

• Total volume of solid will equal to sum of volumes of cone & hemisphere.

$\implies{\rm }$ Cone = 1/3π1¹1

$\implies{\rm }$ π/3 cm³.......i

$\implies{\rm }$ Hemisphere = 2/3π1³

$\implies{\rm }$ 2π/3 cm³......ii

Adding both equations

➮ π/3 + 2π/3

➮ 3π/3

➮ π cm³

Hence, volume of solid will be π cm³.

Answer 2

Given :

• Radius of cone = 1 cm

• Height of cone = 1 cm

To Find :

• Find the volume of the solid in terms of pie.

Solution :

$\sf : \implies \: \: \: \: \: \: \:Volume \: of \: cone = \frac{1}{3}\pi r^{2}h \\ \\ \\ \sf : \implies \: \: \: \: \: \: \:Volume \: of \: cone \: = \frac{1}{3} \times \pi \times 1^{2} \times 1 \\ \\\\ \sf : \implies \: \: \: \: \: \: \:Volume \: of \: cone \:= \frac{1}{3} \pi</p><p> \:$

$\sf : \implies \: \: \: \: \: \: \: Volume \: of \: hemisphere = \frac{2}{3}\pi r^{3} \\ \\ \\ \sf : \implies \: \: \: \: \: \: \: Volume \: of \: hemisphere = \frac{2}{3}\pi$

$\sf : \implies \: \: \: \: \: \: \: Total \: volume =\frac{1}{3}\pi +\frac{2}{3}\pi \\\\ \\ \sf : \implies \: \: \: \: \: \: \:Total \: volume \: = \frac{3}{3}\pi \\ \\ \\ \sf : \implies \: \: \: \: \: \: \:Total \: volume \:= \pi cm^{3}</p><p>$