Question

Height of a solid cylinder is 15 cm and diameter of the base is 7 cm. Two equal conical holes of radii 3 cm and height 4 cm are cut off. Find the volume of the remaining solid.

Answer 1

Answer:

The Volume of the remaining solid is  502.1 cm³.

Step-by-step explanation:

SOLUTION :  

Given :  

Height of the solid cylinder, H = 15 cm

Diameter of the solid cylinder = 7cm

Radius of the solid cylinder , R = 7/2 = 3.5 cm

Height of a conical hole ,h = 4 cm

Radius of a conical hole , r = 3 cm

Volume of the remaining solid = Volume of solid Cylinder - 2 ×  volume of conical hole

= πR²H - 2 ×  ⅓ πr²h

= π(R²H - 2 × ⅓ r²h)

= π (3.5 × 3.5 × 15 - 2 × ⅓ × 3 × 3 × 4)

= π(3.5 × 3.5 × 15 - 2 × 3 × 4)

= π (183 .75 - 24)

= 22/7 × 159.75

= 3,514.5/7  = 502.1 cm³

Volume of the remaining solid = 502.1 cm³

Hence, the Volume of the remaining solid is  502.1 cm³.

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Answer 2

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Given :  

Height of the solid cylinder, H = 15 cm

Diameter of the solid cylinder = 7cm

Radius of the solid cylinder , R = 7/2 = 3.5 cm

Height of a conical hole ,h = 4 cm

Radius of a conical hole , r = 3 cm

$<b>Volume of the remaining solid = Volume of solid Cylinder - 2 ×  volume of conical hole<b>$

= πR²H - 2 ×  ⅓ πr²h

= π(R²H - 2 × ⅓ r²h)

= π (3.5 × 3.5 × 15 - 2 × ⅓ × 3 × 3 × 4)

= π(3.5 × 3.5 × 15 - 2 × 3 × 4)

= π (183 .75 - 24)

= 22/7 × 159.75

= 3,514.5/7  = 502.1 cm³

Volume of the remaining solid = 502.1 cm³

Hence, the Volume of the remaining solid is  502.1 cm³.