the length of the arc of a circle of radian 6 cm subtending an angle of 30' at the centre of the circle is?
Answers
Answer:
Appropriate Question :-
The area of the base of a conical solid is 2464 cm² and its volume is 17248 cm³. Find the curved surface area of the solid.
Given :-
The area of the base of a conical solid is 2464 cm² and its volume is 17248 cm³.
To Find :-
What is the curved surface area of the solid.
Formula Used :-
\clubsuit♣ Volume Of Cone Formula :
\mapsto \sf\boxed{\bold{\pink{Volume_{(Cone)} =\: \dfrac{1}{3}{\pi}r^2h}}}↦Volume(Cone)=31πr2h
\clubsuit♣ Area of Circle Formula :
\begin{gathered}\mapsto \sf\boxed{\bold{\pink{Area_{(Circle)} =\: {\pi}r^2}}}\\\end{gathered}↦Area(Circle)=πr2
\clubsuit♣ Curved Surface Area Of Cone Formula :
\begin{gathered}\mapsto \sf\boxed{\bold{\pink{C.S.A_{(Cone)} =\: {\pi}rl}}}\\\end{gathered}↦C.S.A(Cone)=πrl
where,
π = pie or 22/7
r = Radius
h = Height
l = Slant Height
Solution :-
First, we have to find the radius :
Given :
Area = 2464 cm²
According to the question by using the formula we get,
\implies \sf \dfrac{22}{7} \times r^2 =\: 2464⟹722×r2=2464
\implies \sf r^2 =\: \dfrac{2464 \times 7}{22}⟹r2=222464×7
\implies \sf r^2 =\: \dfrac{\cancel{17248}}{\cancel{22}}⟹r2=2217248
\implies \sf r^2 =\: 784⟹r2=784
\implies \sf r =\: \sqrt{784}⟹r=784
\implies \sf\bold{\green{r =\: 28\: cm}}⟹r=28cm
Now, we have to find the height :
Given :
Volume = 17248 cm³
Radius = 28 cm
According to the question by using the formula we get,
\implies \sf \dfrac{1}{3} \times \dfrac{22}{7} \times (28)^2 \times h =\: 17248⟹31×722×(28)2×h=17248
\implies \sf \dfrac{22}{21} \times 784 \times h =\: 17248⟹2122×784×h=17248
\implies \sf \dfrac{17248}{21} \times h =\: 17248⟹2117248×h=17248
\implies \sf h =\: \dfrac{\cancel{17248} \times 21}{\cancel{17248}}⟹h=1724817248×21
\implies \sf \bold{\green{h =\: 21\: cm}}⟹h=21cm
Now, we have to find the value of slant height :
As we know that,
\clubsuit♣ Pythagoras Theorem Formula :
\begin{gathered}\mapsto \sf\boxed{\bold{\pink{l =\: \sqrt{r^2 + h^2}}}}\\\end{gathered}↦l=r2+h2
where,
l = Slant Height
r = Radius
h = Height
Given :
Radius = 28 cm
Height = 21 cm
According to the question by using the formula we get,
\begin{gathered}\implies \sf l =\: \sqrt{(28)^2 + (21)^2}\\\end{gathered}⟹l=(28)2+(21)2
\implies \sf l =\: \sqrt{784 + 441}⟹l=784+441
\implies \sf l =\: \sqrt{1225}⟹l=1225
\implies \sf\bold{\green{l =\: 35\: cm}}⟹l=35