Question

Find the slant height and vertical height of a cone with radius 5.6cm and curved surface area 158.4cm2

Answer 1

Step-by-step explanation:

C.S.A = 2πrh

158.4cm2 = 2×22/7×5.6×h

158.4cm2 = 44×0.8×h

158.4cm2= 35.2× h

158.4/35.2= h

4.5cm= h(vertical height)

l^2=r^2+h^2

l^2=5.6 ^2+4.5^2

l^2= 31.36+ 20.25

l^ 2= 51.61

l= √51.6

l= 7.18 approx ( l= slant height)

{my answer is right ir not}

Answer 2

Given :

• Radius of cone = 5.6cm  (r)
• Curved surface area of cone = 158.4 cm²  (CSA)

To find :

• Slant height  (l)
• Vertical height  (h)

Solution :

• CSA of cone → (πrl) = 158.4cm²
• ²²⁄₇ × 5.6 × l = 158.4
• l = 158.4 × 7 ÷ 22 × 5.6
• l = ¹⁸⁄₂ l = 9

∴ The slant height is 9cm

• We know :
• l² = r² + h²      (Pythagoras Theorem)
• h² = l² - r²

→ Where h is height, r is radius and l is slant height

• h² = 9² - 5.6²
• h² = 81 - 31.36
• h² = 49.64
• h² = √49.64
• h = 7.05

∴ The vertical height is 7.05cm

Know more :

• Volume of cone = ⅓ πr²h
• Total surface area of cone = πr (r + l)