Question

a large right circular cone is made out of a solid cube of Edge 9 cm find the volume of the remaining solid

Answer 1

Answer:

Volume of remaining solid would be $538.15\text{ cm}^3$

Step-by-step explanation:

A large right circular cone is made out from a solid cube of Edge 9 cm.

Height of cone would be equal to edge of cube (h) = 9 cm

Diameter of circular base of cone is equal to edge of cube = 9 cm

Radius (r) = d/2 = 4.5 cm  

Edge of cube (a) = 9 cm

Volume of remaining solid = Volume of cube - Volume of cone

Formula of volume of solids.

$\text{Volume of cube}=a^3$

$\text{Volume of cone}=\frac{1}{3}\pi r^2h$

$\text{Volume of remaining solid }=a^3-\frac{1}{3}\pi r^2h\Rightarrow 9^3-\frac{1}{3}\pi (4.5)^2\times 9$

Volume of remaining solid = 729 - 190.85 = 538.15 cubic cm

Thus, Volume of remaining solid would be $538.15\text{ cm}^3$

Answer 2

a large right circular cone is made out of solid cube of edge 9cm .

radius of cone , r = half of edge length of cube
= 9cm/2 = 4.5cm
length of cone ,h = edge length of cube
= 9cm

so, volume of cone = 1/3 πr²h
= 1/3 × 3.14 × (4.5)² × 9
= 3 × 3.14 × 20.25
= 199.755 cm³

volume of solid cube = a³
= (9cm)³ = 729 cm³

so, volume of remaining part of solid cube = volume of solid cube - volume of cone
= 729 -199. 755
= 538.245 cm³