The lateral surface area of a cone is 550cm². If the diameter of the cone is 14cm, then the height of the cone is:
- A24 cm
- B12.5 cm
- C12 cm
- D25 cm
Solution & Step-by-step Explanation
Given:
Lateral Surface Area (LSA) = 550cm
2
Diameter = 14cm⟹Radius (r)=
2
14
=7cm
The formula for the lateral surface area of a cone is:
LSA=πrl
Where l is the slant height.
Substituting the known values (π≈
7
22
):
550=
7
22
×7×l
550=22×l
l=
22
550
=25cm
The formula relating radius (r), height (h), and slant height (l) is:
l
2
=r
2
+h
2
25
2
=7
2
+h
2
625=49+h
2
h
2
=625−49=576
h=
576
=24cm
The height of the cone is 24 cm.
Lateral Surface Area (LSA) = 550cm
2
Diameter = 14cm⟹Radius (r)=
2
14
=7cm
The formula for the lateral surface area of a cone is:
LSA=πrl
Where l is the slant height.
Substituting the known values (π≈
7
22
):
550=
7
22
×7×l
550=22×l
l=
22
550
=25cm
The formula relating radius (r), height (h), and slant height (l) is:
l
2
=r
2
+h
2
25
2
=7
2
+h
2
625=49+h
2
h
2
=625−49=576
h=
576
=24cm
The height of the cone is 24 cm.