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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• $\sf{Radius=5.4cm}$
• $\sf{Height=3.28cm}$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answer 2

Solution :-

Area of circular base = πr²

Area = 22/7 × (3.1)²

Area = 30 cm(approximate)

ii) TSA =  2πr(r + h)

TSA = 2 × 3.14 × 3.1(3.1 + 5.16)

TSA = 2 × 3.14 × 3.1(8.16)

TSA = 158 cm²

iii) 2πr²

2 × 3.14 × 3.1²

6.28 × 9.61

60 cm³

iv) Volume = πr²h

= 3.14 × (3.1)² × 5.16

= 3.14 × 9.61 × 5.16

= 155.7 cm³

v) LSA = 2πrh

LSA = 2 × 3.14 × 3.1 × 5.16

LSA = 100 cm