Question

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

Answer 1

Answer:

7.05

Step-by-step explanation:

Radius =5.6 cm, vertical height =h, slant height = l

Curved Surface Area of cone =πrl=158.4cm

2

⇒

7

22

×5.6×l=158.4

⇒l=

22×5.6

158.4×7

=

2

18

=9 cm

We know l

2

=r

2

+h

2

Thus h

2

=l

2

−r

2

=9

2

−(5.6)

2

=81−31.36

=49.64

h=

49.64

h=7.05 cm (approx.)

Answer 2

✯Given✯

➙ Radius of Cone = 5.6cm

➙ Let vertical height be = h

➙ Let slant height be = l

➙ Curved surface area of Cone = 158.4cm² (πrl)

✮Solution✮

➺ πrl = 158.4

➺ ²²⁄₇ × 5.6 × l = 158.4

➺ l = 158.4 × 7 ÷ 22 × 5.6

➺ Slant height (l) = 9cm

✬We have a relation between l , r and h✬

→ l² = r² + h²             (Pythagoras Theorem)

→ h² = l² - r²

→ h² = 9² - 5.6²

→ 81 - 31.36

→ h² = 49.64

→ h =√49.64

→ Height (h) = 7.09cm

✭Learn more✭

⇾ Volume of Cone:-

• ⅓ πr²h

⇾ Curved surface area of Cone:-

• πrl

⇾ Total surface area of Cone:-

• πr (l+r)

→ l is slant height

→ r is radius

→ π is ²²⁄₇