Question

The lateral area of a cone is 9.81 in. The radius is 1.4 in. Find the slant height.

Answer 1

As Per Provided Information

• Lateral area of cone is 9.81 in
• Radius of cone is 1.4 in

We have been asked to determine the slant height of the cone .

Formula used to calculate the lateral area of a cone is

`\boxed{\bf \: \purple{ Lateral \: Area _((Cone)) \: = \pi\:rl}}`

here

l denote slant height

r denote radius

Substituting the value we obtain

`\longrightarrow\tt \: 9.81 = 3.14 * 1.4 * l \\ \\ \\ \longrightarrow\tt \:9.81 = 4.396 * l \\ \\ \\ \longrightarrow\tt \: \cfrac{9.81}{4.396} = l \\ \\ \\ \longrightarrow\tt \: \: l \: = \cfrac{9.81}{4.396} \\ \\ \\ \longrightarrow\tt \: \: l \: = \cancel\cfrac{9.81}{4.396} \\ \\ \\ \longrightarrow\tt \: \: l \: = 2.23 \:inch \: \: (approx)`

Therefore,

• Slant height of the cone is 2.23 in .