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.
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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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Answered by
2
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
= 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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