The radius and height of a right circular cone are in the ratio 4:3 and it's volume is 2156 cu. cm. Find the curved surface area and total surface area of the cone.
Answers
Answer:
Curved surface area of cone = 770 cm²
Total Surface area of cone = 1386 cm²
Step-by-step explanation:
The radius and height of a right circular cone are in the ratio 4:3 and it's volume is 2156 cu. cm. Find the curved surface area and total surface area of the cone
Volume of a cone = (1/3)π r² h
r = Radius
h = Height
Let say radius = 4x cm
then height = 3x cm
Volume of a cone = (1/3) (22/7) (4x)² (3x)
= (22/7) (16) x³
(22/7) (16) x³ = 2156
=> x³ = (2156 * 7) / (22 * 16)
=> x³ = 98 * 7 / 16
=> x³ = 49 * 7 / 8
=> x³ = 7³/2³
=> x = 7/2
Radius = 4x = 4*7/2 = 14cm
Height = 3*7/2 = 10.5 cm
Slant Height = l cm
l² = r² + h²
=> l² = 14² + (10.5)²
=> l² = 196 + 110.25
=> l² = 306.25
=> l = 17.5 cm
Curved Surface Area = π r l
= (22/7) * 14 * 17.5
= 44 * 17.5
= 770 cm²
Curved surface area of cone = 770 cm²
Total Surface Area = π r² + π r l
= (22/7) * 14² + 770
= 616 + 770
= 1386 cm²
Total Surface area of cone = 1386 cm²
Answer:
Let the radius be 4x and height be 3x of the right circular cone.
We have,
Area of the right circular cone = 2156 cm³
★ According to Question now,
➨ Volume of cone = ⅓ πr²h
➳ 2156 = 1/3 × 22/7 × (4x)² × (3x)
➳ 2156 = 1/3 × 22/7 × 16x² × 3x
➳ 2156 = 22/7 × 16x² × x
➳ 16x³ = 2156 × 7/22
➳ x³ = 98 × 7/16
➳ x³ = 7 × 7 × 7/2 × 2 × 2
➳ x = 7/2
➳ x = 3.5 cm
Therefore,
Radius = 4x = 4(3.5) = 14 cm
Height = 3x = 3(3.5) = 10.5 cm
______________________
➳ Slant height (l)² = r² + h²
➳ l² = (14)² + (3.5)²
➳ l² = 196 + 110.25
➳ l² = 306.25
➳ l = √306.25
➳ Slant Height (l) = 17.5 cm
_____________________
➳ CSA of cone = πrl
➳ CSA of cone = 22/7 × 14 × 10.5
➳ CSA of cone = 22 × 2 × 10.5
➳ CSA of cone = 44 × 10.5
➳ CSA of cone = 770 cm²
___________________________
➳ TSA of cone = πr² + πrl
➳ TSA of cone = 22/7 × 14² + 770
➳ TSA of cone = 616 + 770
➳ TSA of cone = 1386 cm²