[tex] \large\underline{ \sf Question :-}[/tex]
⠀
The curved surface area of a cylinder is 176 cm² and its area of the base is 38.5 cm². Find the volume of the cylinder. (Take π = 22/7)
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[tex] \large\underline{ \sf Question :-}[/tex]
⠀
The curved surface area of a cylinder is 176 cm² and its area of the base is 38.5 cm². Find the volume of the cylinder. (Take π = 22/7)
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Verified answer
Answer:
Given :-
To Find :-
Solution :-
First, we have to find the radius of a cylinder :
Given :
According to the question by using the formula we get,
[tex]\bigstar \: \: \sf\boxed{\bold{Area\: of\: Base_{(Cylinder)} =\: {\pi}r^2}}\: \: \: \bigstar\\[/tex]
where,
So,
[tex]\implies \bf Area\: of\: Base_{(Cylinder)} =\: {\pi}r^2\\[/tex]
[tex]\implies \sf 38.5 =\: \dfrac{22}{7} \times r^2\\[/tex]
[tex]\implies \sf 38.5 \times \dfrac{7}{22} =\: r^2\\[/tex]
[tex]\implies \sf \dfrac{269.5}{22} =\: r^2\\[/tex]
[tex]\implies \sf 12.25 =\: r^2[/tex]
[tex]\implies \sf \sqrt{12.25} =\: r[/tex]
[tex]\implies \sf 3.5 =\: r[/tex]
[tex]\implies \sf\bold{r =\: 3.5\: cm}\\[/tex]
Hence, the radius of a cylinder is 3.5 cm .
Now, we have to find the height of a cylinder :
Given :
According to the question by using the formula we get,
[tex]\bigstar \: \: \sf\boxed{\bold{C.S.A._{(Cylinder)} =\: 2{\pi}rh}}\: \: \: \bigstar\\[/tex]
where,
So,
[tex]\implies \bf C.S.A._{(Cylinder)} =\: 2{\pi}rh\\[/tex]
[tex]\implies \sf 176 =\: 2 \times \dfrac{22}{7} \times 3.5 \times h\\[/tex]
[tex]\implies \sf 176 =\: \dfrac{44}{7} \times 3.5 \times h\\[/tex]
[tex]\implies \sf 176 =\: \dfrac{154}{7} \times h\\[/tex]
[tex]\implies \sf 176 \times \dfrac{7}{154} =\: h\\[/tex]
[tex]\implies \sf \dfrac{1232}{154} =\: h\\[/tex]
[tex]\implies \sf 8 =\: h\\[/tex]
[tex]\implies \sf\bold{h =\: 8\: cm}\\[/tex]
Hence, the height of a cylinder is 8 cm .
Now, we have to find the volume of a cylinder :
Given :
According to the question by using the formula we get,
[tex]\bigstar \: \: \sf\boxed{\bold{Volume_{(Cylinder)} =\: {\pi}r^2h}}\: \: \: \bigstar\\[/tex]
So,
[tex]\dashrightarrow \bf Volume_{(Cylinder)} =\: {\pi}r^2h\\[/tex]
[tex]\dashrightarrow \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times (3.5)^2 \times 8\\[/tex]
[tex]\dashrightarrow \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times (3.5 \times 3.5) \times 8\\[/tex]
[tex]\dashrightarrow \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times 12.25 \times 8\\[/tex]
[tex]\dashrightarrow \sf Volume_{(Cylinder)} =\: \dfrac{22}{7} \times 98\\[/tex]
[tex]\dashrightarrow \sf Volume_{(Cylinder)} =\: \dfrac{2156}{7}\\[/tex]
[tex]\dashrightarrow \sf Volume_{(Cylinder)} =\: 308\: cm^2\\[/tex]
[tex]\sf\bold{\underline{\therefore\: The\: volume\: of\: the\: cylinder\: is\: 308\: cm^2\: .}}\\[/tex]