Question

From a solid right circular cylinder with height 15 cm and radius 7 cm, a right circular cone of the same height and base is removed. find the volume of remaining solid ​

Answer 1

QuestioN :

From a solid right circular cylinder with height 15 cm and radius 7 cm, a right circular cone of the same height and base is removed. find the volume of remaining solid ​

GiveN :

• From a solid right circular cylinder with height 15 cm and radius 7 cm, a right circular cone of the same height and base is removed.

To FiNd :

• The volume of remaining solid ​

ANswer :

The Volume of the remaining solid is 1540 cm³.

SolutioN :

For Cylinder,

We are given with the dimensions as:-

• Height = 15 cm
• Radius = 7 cm

We know,

• Volume of cylinder = πr²h cu.units

Hence,

Volume of cylinder = 22/7 × (7)² × 15

Volume = 22/7 × 49 × 15

Volume = 22 × 7 × 15

Volume = 2310 cm³

∴ Volume of the cone is 2310 cm³.

For Cone,

We are give with the dimensions of cone as:-

• Height = 15 cm
• Radius = 7 cm

We know,

• Volume of cone = 1/3 πr²h cu.units

Hence,

Volume of cone = 1/3 × 22/7 × (7)² × 15

Volume = 1 × 22/7 × 49 × 5

Volume = 22 × 7 × 5

Volume = 770 cm³

∴ Volume of the cone is 770 cm³.

Now,

Volume of remaining solid is as follows:-

Volume of cylinder - Volume of cone

= 2310 - 770

= 1540 cm³

∴Hence, Volume of the remaining solid is 1540 cm³.

Answer 2

${\huge{\star{\underbrace{\tt{\red{Answer}}}}}}{\huge{\star}}$

Given :

• Height of cylinder = 15cm
• Radius of cylinder = 7cm
• Height and base of cone are same as cylinder

To find :

• Volume of remaining solid

Solution :

We know that ,

${\boxed{\sf \star \purple \ Volume \ of \ cylinder \ = \ \pi {r}^{2} h}}$

${\implies}$ Volume of cylinder = ${\frac{22}{\cancel7} \times 15 \times 7 \times \cancel7}$

${\implies}$ Volume of cylinder = 22 × 7 ×15

${\implies}$ Volume of cylinder = 2310cm³

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Since , the height and base of cone are same as that of cylinder

• height of cone = 15cm
• base of cone = 7cm

${\boxed{\sf \green \star \ Volume \ of \ cone \ = \ \frac{1}{3} \pi {r}^{2} h}}$

${\implies}$ Volume of cone = ${\frac{1}{\cancel3} \times \cancel{2310}}$

[Note] - Value of πr²h is already finded above.

${\implies}$ Volume of cone = 770cm³

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${\leadsto \sf \ Volume \ of \ remaining \ solid \ = \ Volume \ of \ cylinder \ - \ Volume \ of \ cone}$

${\leadsto}$ Volume of remaining solid = 2310 - 770

${\leadsto}$ Volume of remaining solid = 1540cm³

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