Question

$\large{\dag \; {\underline{\underline{\orange{\pmb{\frak{ \; Question \; :- }}}}}}}$

Find the volume, curved surface area and total surface area of each of the cylinders whose dimensions are as follows :

(i) radius of the base = 7 cm and height = 50 cm
(ii) radius of the base = 5.6 m and height = 1.25 m
(iii) radius of the base = 14 dm and height = 15 m


$\\ {\underline{\rule{200pt}{5pt}}}$

$\large{\dag \; {\underline{\underline{\green{\pmb{\frak{ \; Note \; :- }}}}}}}$

$\dashrightarrow$ Answer with proper Explaination .
$\dashrightarrow$ Use latex to give the Answer .
$\dashrightarrow$ ${\red{\sf{ No \; Spams }}}$


$\\ {\underline{\rule{200pt}{5pt}}}$

​

Answer 1

Question 1

We know that volume of the cylinder = πr2h

Here r = 7cm h = 50cm

V = 22/7 × 7 × 7 × 50

V = 22 × 7 × 50

V = 7700 cm3

Also we know that curved surface area of cylinder = 2πrh

Curved surface area = 2 × 22/7 × 7 × 50

Curved surface area = 2200 cm2

We know that total surface area of cylinder = 2πr(r + h) Total surface area = 2 × 22/7 × 7 (7 + 50)

Total surface area = 2580 cm2

Question 2

We know that volume of the cylinder = πr²h

Here r = 5.6m H = 1.25m

v = 22/7 × 5.6 × 5.6 × 1.25

V = 122.2m³

Also we know that curved surface area of cylinder = 2πrh

curved surface area = 2×22/7 × 5.6 × 1.25

curved surface area = 44m²

We know that total surface area of cylinder = 2πr(r+h)

Total surface area = 2×22/7 ×5.6 (5.6+1.25)

Total surface area = 241.12m²

Question 3

We know that volume of the cylinder =πr²h

Here r=14 dm=1.4 m, h=15 m

So,

V=22/7×1.4×1.4×15

V=92.4 mm³

Also we know that curved surface area of cylinder =2πrh

So,

Curved surface area =2×22/7×1.4×15

Curved surface area =132 m²

We know that total surface area of cylinder =2π(r+h)

So,

Total surface area =2×22/7×1.4(1.4+15)

Total surface area =144.32 m²

Answer 2

Answer:

i) Vol. = 7700 cm³, CSA = 2200 cm², TSA = 2508 cm²

ii) Vol. = 123.2 m³, CSA = 44 m², TSA = 241.12 m²

iii) Vol. = 92.4 m³, CSA = 132 m², TSA = 144.32 m ²

$\rule{70mm}{2pt}$

Step-by-step explanation:

Given that (i) radius of the base = 7 cm and height = 50 cm (ii) radius of the base = 5.6 m and height = 1.25 m (iii) radius of the base = 14 dm and height = 15 m.

We need to find out the value of volume, curved surface area and total surface area of cylinder.

Assumption: Let's say that point A and B that are shown in cylinder (refer the attachment) is radius 'r' and BC is height 'h' of the cylinder.

We know that-

$\huge{\underline{\boxed{\red{\sf{Vol.\:of\:cylinder\:=\:\pi r^{2}h}}}}}$

$\huge{\underline{\boxed{\green{\sf{CSA\:of\: cylinder=\:2\pi rh}}}}}$

$\huge{\underline{\boxed{\red{\sf{TSA\:of\:cylinder\:=\:2\pi r(r+h)}}}}}$

(Where Vol. = Volume, CSA = Curved surface area and TSA = Total Surface area)

$\rule{40mm}{1pt}$

Now,

Simply substitute the value of radius and height in above formulas to get the value of vol, CSA and TSA of cylinder.

$\underline{\underline{\orange{\sf{As\:per\:given\:condition:}}}}$

i) radius of the base = 7 cm and height = 50 cm

$\implies\:\sf{Vol.\:=\:22/7\:\times\:(7)^{2}\:\times\:(50)}$

$\implies\:\sf{Vol.\:=\:22/7\:\times\:49\:\times\:50}$

$\implies\:\sf{Vol.\:=\:22(7)(50)}$

$\implies\:\red{\sf{Vol.\:=\:7700cm^{3}}}$

Therefore, the volume of the cylinder is 7700 cm³.

$\implies\:\sf{CSA\:=\:2(22/7)(7)(50)}$

$\implies\:\sf{CSA\:=\:44(50)}$

$\implies\:\red{\sf{CSA\:=\:2200cm^{2}}}$

Therefore, the curved surface area of the cylinder is 2200 cm².

$\implies\:\sf{TSA\:=\:2(22/7)(7)(7+50)}$

$\implies\:\sf{TSA\:=\:44(57)}$

$\implies\:\red{\sf{TSA\:=\:2508cm^{2}}}$

Therefore, the total surface area of cylinder is 2508 cm².

$\rule{40mm}{1pt}$

ii) radius of the base = 5.6 m and height = 1.25 m

$\implies\:\sf{Vol.\:=\:22/7\:\times\:(5.6)^{2}\:\times\:(1.25)}$

$\implies\:\sf{Vol.\:=\:22/7\:\times\:31.36\:\times\:1.25}$

$\implies\:\sf{Vol.\:=\:22(4.48)(1.25)}$

$\implies\:\green{\sf{Vol.\:=\:123.2m^{3}}}$

Therefore, the volume of the cylinder is 123.2 m³.

$\implies\:\sf{CSA\:=\:2(22/7)(5.6)(1.25)}$

$\implies\:\sf{CSA\:=\:44(0.8)(1.25)}$

$\implies\:\green{\sf{CSA\:=\:44m^{2}}}$

Therefore, the CSA of the cylinder is 44 m².

$\implies\:\sf{TSA\:=\:2(22/7)(5.6)(5.6+1.25)}$

$\implies\:\sf{TSA\:=\:44(0.8)(6.85)}$

$\implies\:\green{\sf{TSA\:=\:241.12m^{2}}}$

Therefore, the TSA of the cylinder is 241.12 m².

$\rule{40mm}{1pt}$

(iii) radius of the base = 14 dm and height = 15 m

To convert dm into m. Divide the value by 10. So, 14 dm = 1.4 m.

$\implies\:\sf{Vol.\:=\:22/7\:\times\:(1.4)^{2}\:\times\:(15)}$

$\implies\:\sf{Vol.\:=\:22/7\:\times\:1.96\:\times\:15}$

$\implies\:\sf{Vol.\:=\:22(0.28)(15)}$

$\implies\:\red{\sf{Vol.\:=\:92.4m^{3}}}$

Therefore, the volume of the cylinder is 92.4 m³.

$\implies\:\sf{CSA\:=\:2(22/7)(1.4)(15)}$

$\implies\:\sf{CSA\:=\:44(0.2)(15)}$

$\implies\:\red{\sf{CSA\:=\:132m^{2}}}$

Therefore, the CSA of the cylinder is 132 m².

$\implies\:\sf{TSA\:=\:2(22/7)(1.4)(1.4+15)}$

$\implies\:\sf{TSA\:=\:44(0.2)(16.4)}$

$\implies\:\red{\sf{TSA\:=\:144.32m^{2}}}$

Therefore, the TSA of the cylinder is 144.32 m².