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
I beg u all for help me please​

Answer 1

1. r = 3.1 cm, h = 5.16 cm

1. Area of circular base = πr² = π × (3.1)² = 30.1754 cm²
2. Total surface area = 2πr(r + h) = 2π × 3.1 × (3.1 + 5.16) = 160.8056 cm²
3. Curved surface area = 2πrh = 2 × π × 3.1 × 5.16 = 100.4548 cm²
4. Volume = πr²h = π × (3.1)² × (5.16) = 155.7050 cm³

2. r = 5.4 cm, h = 3.28 cm

1. Area of circular base = πr² = π × (5.4)² = 91.5624 cm²
2. Total surface area = 2πr(r + h) = 2π × 5.4 × (5.4 + 3.28) = 294.3561 cm²
3. Curved surface area = 2πrh = 2 × π × 5.4 × 3.28 = 111.2313 cm²
4. Volume = πr²h = π × (5.4)² × (3.28) = 300.3246 cm³

3. d = 8 cm, r = 8/2 = 4 cm, h = 6.5 cm

1. Area of circular base = πr² = π × (4)² = 50.24 cm²
2. Total surface area = 2πr(r + h) = 2π × 4 × (4 + 6.5) = 263.76 cm²
3. Curved surface area = 2πrh = 2 × π × 4 × 6.5 = 163.28 cm²
4. Volume = πr²h = π × (4)² × (6.5) = 326.56 cm³

Note: Total circular surface area = Total curved surface area = Curved surface area

Answer 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$\sf{Radius=5.4cm}$

$\sf{Height=3.28cm}$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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