Question

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

Answer 1

Answer:

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

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

Therefore,

• Slant height of the cone is 2.23 in .