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.
Answers
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)
=
3
1
πr
2
h
\clubsuit♣ Area of Circle Formula :
\begin{gathered}\mapsto \sf\boxed{\bold{\pink{Area_{(Circle)} =\: {\pi}r^2}}}\\\end{gathered}
↦
Area
(Circle)
=πr
2
\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⟹
7
22
×r
2
=2464
\implies \sf r^2 =\: \dfrac{2464 \times 7}{22}⟹r
2
=
22
2464×7
\implies \sf r^2 =\: \dfrac{\cancel{17248}}{\cancel{22}}⟹r
2
=
22
17248
\implies \sf r^2 =\: 784⟹r
2
=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⟹
3
1
×
7
22
×(28)
2
×h=17248
\implies \sf \dfrac{22}{21} \times 784 \times h =\: 17248⟹
21
22
×784×h=17248
\implies \sf \dfrac{17248}{21} \times h =\: 17248⟹
21
17248
×h=17248
\implies \sf h =\: \dfrac{\cancel{17248} \times 21}{\cancel{17248}}⟹h=
17248
17248
×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=
r
2
+h
2
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=35cm
Now, we have to find the curved surface area of the cone :
Given :
Radius = 28 cm
Slant height = 35 cm
According to the question by using the formula we get,
\begin{gathered}\longrightarrow \sf C.S.A_{(Cone)} =\: \dfrac{22}{7} \times 28 \times 35\\\end{gathered}
⟶C.S.A
(Cone)
=
7
22
×28×35
\longrightarrow \sf C.S.A_{(Cone)} =\: \dfrac{22}{7} \times 980⟶C.S.A
(Cone)
=
7
22
×980
\longrightarrow \sf C.S.A_{(Cone)} =\: \dfrac{21560}{7}⟶C.S.A
(Cone)
=
7
21560
\longrightarrow \sf\bold{\red{C.S.A_{(Cone)} =\: 3080\: cm^2}}⟶C.S.A
(Cone)
=3080cm
2
\therefore∴ The curved surface area or CSA of cone is 3080 cm².
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