the circumference of the base of a cylinder is 176 cm and its height is 65 cm find the volume and lateral surface area of the cylinder
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the circumference of the base of a cylinder is 176 cm and its height is 65 cm find the volume and lateral surface area of the cylinder
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Lateral surface area of a cylinder is given by,
LSA = 2*pi*r*h
Given 2*pi*r = 176 cm
h = 65 cm
Hence LSA = 176*65 cm^2
LSA = 11440 cm^2 or 1.1440 m^2
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Answer:
Volume of the cylinder = [tex]160160 \: cm{}^{3} [/tex]
Lateral surface area of the cylinder = [tex]11440 \: cm {}^{2} [/tex]
Step-by-step explanation:
Let the base radius of the cylinder be r cm
Then circumference of it base = [tex](2\pi \: r) \: cm[/tex]
But circumference of the base = 176 cm
∴ [tex]2\pi \: r = 176[/tex]⇒[tex]2 \times \frac{22}{7} \times r = 176[/tex]
⇒r = [tex](176 \times \frac{7}{44} ) = 28[/tex]
Now, r = 28 cm and h = 65 cm
Volume of the cylinder = [tex](\pi \: r {}^{2} h) \: cubic \: units[/tex]
= [tex]( \frac{22}{7} \times 28 \times 28 \times 65) \: cm {}^{3} = 160160 \: cm {}^{3} [/tex]
Lateral surface area of the cylinder = [tex](2\pi \: rh) \: sq \: units[/tex]
= [tex](2 \times \frac{22}{7} \times28 \times65)cm {}^{3} [/tex]
= [tex]11440 \: cm {}^{2} [/tex]