the circumference of the base of a cone is 44cm and its slant height is 25cm. find the volume and the curved surface area of the cone.
Answers
Círcumfєrєncє σf thє вαsє = 2πr = 44 cm²
Slαnt hєíght ( l ) = 25 cm
wє knσw thαt,
❥ Slαnt hєíght = √ ( r² + h² )
Usíng thє gívєn ínfσrmαtíσn wє cαn fínd σut thє rαdíus σf thє cσnє.
❥ 2πr = 44
❥ r = 44 / 2π
❥ r = 44 × 7/44
❥ r = 7
Suвstítutíng ín thє slαnt hєíght fσrmulα wє gєt,
─━━━━━━⊱✿⊰━━━━━━─
❥ 25 = √ ( 7 )² + h²
squαríng σn вσth sídєs wє gєt,
❥ 25² = 7² + h²
❥ 625 = 49 + h²
❥ 625 - 49 = h²
❥ 576 = h²
❥ h = √576 = 24
Curvєd surfαcє αrєα σf cσnє = πrl
❥ CSA σf cσnє = 22/7 × 7 × 25
❥ CSA σf cσnє = 550 cm²
vσlumє σf cσnє = 1/3 πr²h
❥ vσlumє σf cσnє = 1/3 × 22/7 × 49 × 24
❥ vσlumє σf cσnє = 154/3 × 24
❥ vσlumє σf cσnє = 154 × 8
❥ vσlumє σf cσnє = 1232 cm³
─━━━━━━⊱✿⊰━━━━━━─
Answer:
Volume of cone ≈366.19 & CSA of cone = 293.59
Step-by-step explanation:
the circumference of the base of a cone is 44cm
π r² = 44
r² = 44 / 3.14
r² = 14.01
r = 3.74
Volume of cone = 1/3hπr²
V≈366.19
curved surface area of the cone = πrl
=3.14 * 3.74 * 25
CSA of cone = 293.59