The height of a solid cylinder is 15 cm and the diameter of its base is 7 cm. Two equal conical holes each of radius 3 cm and height 4 cm are cut off. Find the volume of the remaining solid.
Answers
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
Volume of the remaining solid = 502.1 cm³
Hence, the Volume of the remaining solid is 502.1 cm³.
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Answer:
Find the radius of the cylinder:
Radius = Diameter ÷ 2
Radius = 7 ÷ 2 = 3.5 cm
Find the surface area of the cylinder:
Surface area = 2πr² + 2πrh
Surface area = 2π(3.5)² + 2π(3.5)(15) = 407 cm²
Find the slanted height of the conical hole:
a² + b² = c²
c² = 3² + 4²
c² = 25
c = √25
c = 5 cm
Find the area of the base of the cone:
Area = πr²
Area = π(3)² = 198/7 cm²
Find the curved surface area of the cone:
Area = πrl
Area = π(3)(5) = 330/7 cm²
Find the total surface area:
Total Surface area = Total Surface area of cylinder - 2(base of the cone) + 2(curved surface area of the cone)
Total Surface area = 407 - 2(198/7 ) + 2(330/7) = 444.71 cm²
Answer: Total Surface area = 444.71 cm²