Curved surface area of a cone is $308{\text{ c}}{{\text{m}}^2}$ and its slant height is $14{\text{ cm}}$. Find
${\text{(i)}}$ radius of the base
${\text{(ii)}}$ total surface area of the cone.
Last updated date: 28th Mar 2023
•
Total views: 310.8k
•
Views today: 5.90k
Answer
310.8k+ views
Hint- Here, we will be using the formulas for curved surface area and total surface area of the cone.
Given, Curved surface area of a cone is ${{\text{A}}_{\text{c}}} = 308{\text{ c}}{{\text{m}}^2}$ and its slant height is $l = 14{\text{ cm}}$
${\text{(i)}}$ Since, the formula for the curved surface of a cone having radius of the base as $r$ and slant height as $l$ is given by ${{\text{A}}_{\text{c}}} = \pi rl$
Using above formula, we can write
${{\text{A}}_{\text{c}}} = \pi rl \Rightarrow 305 = \dfrac{{22}}{7} \times r \times 14 \Rightarrow r = \dfrac{7}{{22 \times 14}} \times 305 \Rightarrow r = 6.93{\text{ cm}}$
Therefore, the radius of the base of the given cone is 6.93 cm.
${\text{(ii)}}$ Also, we know that the formula for the total surface of a cone having radius of the base as $r$ and slant height as $l$ is given by ${{\text{A}}_{\text{s}}} = \pi {r^2} + \pi rl = \pi r\left( {r + l} \right)$
Using the above formula, we get
${{\text{A}}_{\text{s}}} = \pi r\left( {r + l} \right) = \dfrac{{22}}{7} \times 6.93 \times \left( {6.93 + 14} \right) = \dfrac{{22}}{7} \times 6.93 \times 20.93 = 455.85{\text{ c}}{{\text{m}}^2}$
Therefore, the total surface area of the given cone is $455.85{\text{ c}}{{\text{m}}^2}$.
Note- In these types of problems, we have to make sure that all the units of given values are the same. Also, the total surface area of the cone is the sum of its curved surface area (i.e., $\pi rl$) and the area of the base (i.e., $\pi {r^2}$).
Given, Curved surface area of a cone is ${{\text{A}}_{\text{c}}} = 308{\text{ c}}{{\text{m}}^2}$ and its slant height is $l = 14{\text{ cm}}$
${\text{(i)}}$ Since, the formula for the curved surface of a cone having radius of the base as $r$ and slant height as $l$ is given by ${{\text{A}}_{\text{c}}} = \pi rl$
Using above formula, we can write
${{\text{A}}_{\text{c}}} = \pi rl \Rightarrow 305 = \dfrac{{22}}{7} \times r \times 14 \Rightarrow r = \dfrac{7}{{22 \times 14}} \times 305 \Rightarrow r = 6.93{\text{ cm}}$
Therefore, the radius of the base of the given cone is 6.93 cm.
${\text{(ii)}}$ Also, we know that the formula for the total surface of a cone having radius of the base as $r$ and slant height as $l$ is given by ${{\text{A}}_{\text{s}}} = \pi {r^2} + \pi rl = \pi r\left( {r + l} \right)$
Using the above formula, we get
${{\text{A}}_{\text{s}}} = \pi r\left( {r + l} \right) = \dfrac{{22}}{7} \times 6.93 \times \left( {6.93 + 14} \right) = \dfrac{{22}}{7} \times 6.93 \times 20.93 = 455.85{\text{ c}}{{\text{m}}^2}$
Therefore, the total surface area of the given cone is $455.85{\text{ c}}{{\text{m}}^2}$.
Note- In these types of problems, we have to make sure that all the units of given values are the same. Also, the total surface area of the cone is the sum of its curved surface area (i.e., $\pi rl$) and the area of the base (i.e., $\pi {r^2}$).
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
