Question

16
Following are the radius and height of cylinders,
(a) radius 3.1 cm
height 5.16 cm
(b) radius 5.4 cm
height 3.28 cm
(c) diameter 8 cm
height 6.5 cm
Find
(i) The area of the circular base
(ii) The total surface area
iii)The total circular surface area
(iv) The volume of the cylinder
v)The total curved surface area​

Answer 1

$\sf\small\underline\green{Given:-}$

$\sf{\implies Radius\:_{(cylinder)}=3.1cm}$

$\sf{\implies Height\:_{(cylinder)}=5.16cm}$

$\sf\small\underline\green{To\: Find:-}$

$\sf\small\underline\green{(i)Area\:_{(circular\:base)}}$

$\tt{\implies \pi\:r^2}$

$\tt{\implies \dfrac{22}{7}\times\:(3.1)^2}$

$\tt{\implies \dfrac{22*3.1*3.1}{7}}$

$\tt{\implies \dfrac{242.42}{7}}$

$\tt{\implies 30.20\:cm^2}$

$\sf\small\underline\green{(ii)Area\:_{(total\:surface)}}$

$\tt{\implies 2\pi\:r\:h+2\pi\:r^2}$

$\tt{\implies 2\pi\:r(h+r)}$

$\tt{\implies 2*\pi*3.1(5.16+3.1)}$

$\tt{\implies 6.2\pi*8.26}$

$\tt{\implies \dfrac{6.2*22*8.26}{7}}$

$\tt{\implies 160.952\:cm^2}$

$\sf\small\underline\green{(iii)Area\:_{(total\:circular\:base)}}$

$\tt{\implies 2\pi\:r^2}$

$\tt{\implies 2*\dfrac{22}{7}*(3.1)^2}$

$\tt{\implies \dfrac{2*22*3.1*3.1}{7}}$

$\tt{\implies \dfrac{422.84}{7}}$

$\tt{\implies 60.40\:cm^2}$

$\sf\small\underline\green{(iv) Volume\:_{(Cylinder)}:-}$

$\tt{\implies \pi\:r^2\:h}$

$\tt{\implies \dfrac{22}{7}*(3.1)^2*5.16}$

$\tt{\implies \dfrac{22*3.1*3.1*5.16}{7}}$

$\tt{\implies \dfrac{1090.92}{7}}$

$\tt{\implies 155.84\:cm^3}$

$\sf\small\underline\green{(v) Area\:_{(C.S.A\:Cylinder)}:-}$

$\tt{\implies 2\pi\:r\:h}$

$\tt{\implies 2*\dfrac{22}{7}*3.1*5.16}$

$\tt{\implies \dfrac{2*22*3.1*5.16}{7}}$

$\tt{\implies \dfrac{703.824}{7}}$

$\tt{\implies 100.54\:cm^2}$

$\sf\small\underline\green{To\: Find:-}$

$\sf\small\underline\red{Calculation\:for\:(b):-}$

$\sf{Radius=5.4cm}$

$\sf{Height=3.28cm}$

$\sf\small\underline\green{(i)Area\:_{(circular\:base)}}$

$\tt{\implies \pi\:r^2}$

$\tt{\implies \dfrac{22}{7}\times\:(3.28)^2}$

$\tt{\implies \dfrac{22*3.28*3.28}{7}}$

$\tt{\implies \dfrac{236.68}{7}}$

$\tt{\implies 33.81\:cm^2}$

$\sf\small\underline\green{(ii)Area\:_{(total\:surface)}}$

$\tt{\implies 2\pi\:r\:h+2\pi\:r^2}$

$\tt{\implies 2\pi\:r(h+r)}$

$\tt{\implies 2*\pi*3.28(5.4+3.28)}$

$\tt{\implies 6.56\pi*8.68}$

$\tt{\implies \dfrac{6.56*22*8.68}{7}}$

$\tt{\implies 178.95\:cm^2}$

$\sf\small\underline\green{(iii)Area\:_{(total\:circular\:base)}}$

$\tt{\implies 2\pi\:r^2}$

$\tt{\implies 2*\dfrac{22}{7}*(3.1)^2}$

$\tt{\implies \dfrac{2*22*3.28*3.28}{7}}$

$\tt{\implies \dfrac{473.36}{7}}$

$\tt{\implies 67.62\:cm^2}$

$\sf\small\underline\green{(iv) Volume\:_{(Cylinder)}:-}$

$\tt{\implies \pi\:r^2\:h}$

$\tt{\implies \dfrac{22}{7}*(3.28)^2*5.4}$

$\tt{\implies \dfrac{22*3.28*3.28*5.4}{7}}$

$\tt{\implies \dfrac{1278.09}{7}}$

$\tt{\implies 182.58\:cm^3}$

$\sf\small\underline\green{(v) Area\:_{(C.S.A\:Cylinder)}:-}$

$\tt{\implies 2\pi\:r\:h}$

$\tt{\implies 2*\dfrac{22}{7}*3.28*5.4}$

$\tt{\implies \dfrac{2*22*3.28*5.4}{7}}$

$\tt{\implies \dfrac{779.32}{7}}$

$\tt{\implies 111.33\:cm^2}$