Question

MATHEMATICS-IX]
29. From a solid circular cylinder with height 10 cm and radius of base 6 cm, a right circular cone of the same
height and same base is removed. Find the volume of remaining solid.​

Answer 1

Answer:

$\bigstar{\bold{Volume\:of\:remaining\:solid=753.6\:cm^{3} }}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Height of cylinder = 10 cm
• Radius of cylinder = 6 cm
• Height of cone = 10 cm
• Radius of cone = 6 cm

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Volume of the remaining solid

$\Large{\underline{\underline{\bf{Solution:}}}}$

➳ First we have to find the volume of the cylinder.

➳ Volume of a cylinder is given by,

    Volume of a cylinder = π r² h

➳ Substituting the data,

    Volume of the cylinder = 3.14 × 6 × 6 × 10

    Volume of the cylinder = 18.84 × 60

    Volume of the cylinder = 1130.4 cm³

➳ Hence volume of the cylinder is 1130.4 cm³

➳ Now we have to find the volume of the cone

➳ Volume of a cone is given by,

   Volume of a cone = 1/3 × π × r² × h

➳ Substitute the data,

    Volume of the cone = 1/3 × 3.14 × 6 × 6 × 10

    Volume of the cone = 6.28 × 60

    Volume of the cone = 376.8 cm³

➳ Hence the volume of the cone is 376.8 cm³

➳ Now the volume of the remaining solid is given by,

    Volume of remaining solid = Volume of cylinder - Volume of cone

➳ Substitute the data,

    Volume of remaining solid = 1130.4 - 376.8

    Volume of remaiing solid = 753.6 cm³

➳ Hence volume of the remaining solid is 753.6 cm³

    $\boxed{\bold{Volume\:of\:remaining\:solid=753.6\:cm^{3} }}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

➳ The volume of a cylinder is given by,

     Volume of a cylinder = π r² h

➳ Volume of a cone is given by,

      Volume of a cone = 1/3 × π × r² × h

Answer 2

Answer :-

✳ Volume of Remaining Solid - 753.6 cm³

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★ Concept :-

Here the concept of Volume of two solids is used. According to this, if we are given two solids and one both are in relation to each other by removal or joining, the area of the remaining solid can be simply obtained.

________________________________

★Solution :-

Given,

• Height of the cylinder = 10 cm
• Radius of base of cylinder = 6 cm
• Height of cone = 10 cm
• Radius of base of cone = 10 cm

_______________________________

Here if we find the Volume of Cylinder and from it if we subtract the Volume of Cone, we can easily obtain the Volume of Remaining Solid.

Then,

▶Volume of Cylinder = π r²h

By applying the given value, we get,

▶ Volume of Cylinder = 3.14 × 6 × 6 × 10

Note* here we are using the value of π as 3.14 for easier calculation. You can use 22/7 also.

▶ Volume of Cylinder = 3.14 × 360

▶ Volume of Cylinder = 1130.4 cm³

Hence the volume of Cylinder = 1130.4 cm³

________________________________

Now we need to find the volume of Cone. This is given by,

▶Volume of Cone = ⅓(π r²h)

By applying the values, we get,

▶Volume of Cone = ⅓(3.14 × 6 × 6 × 10)

▶Volume of Cone = 6.28 × 60

▶Volume of Cone = 376.8 cm³

Hence Volume of Cone = 376.8 cm³

_______________________________

Now we can easily find our the volume of remaining solid by the concept discussed above.

✒ Volume of Remaining Solid = Volume of Cylinder - Volume of Cone

✒ Volume of Remaining Solid = 1130.4 cm³ - 376.8 cm³

✒ Volume of Remaining Solid = 753.6 cm³

Hence, finally we get, the volume of remaining solid = 753.6 cm³.

___________________________

★ More to know :-

• Volume of cube = (Side)³

• Volume of Cuboid = Length × Breadth × Height

• Volume of Hemisphere = ⅔ (π r³)

• The use of correct unit is necessary here. Since we are finding Volume, here the multiplication of three dimensions of Length takes place so the unit should be (unit)³ . But when we are finding Total Surface Area or Lateral Surface Area,we are multiplying two dimensions of length so the unit comes to be (unit)².