Question

find the total surface area of a right circular cylinder whose base has radius 7 cm and height 8 cm 2) find the volume of a cylinderical can height 21 cm and base radius 8 cm

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Answer 1

Question 1 :-

Given:-

• Radius of cylinder
• Height of cylinder

To find:-

• Total surface area of right a circular cylinder.

Solution:-

Radius of base:- 7 cm

Height:- 8 cm

Total surface area:- 2πr(h+r)

2×22÷7×7(7+8)

2×22÷7×7×15

660 cm²

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Question 2 :-

Given:-

• Height of the cylindrical can
• Radius

To find:-

• Volume of the cylindrical can

Solution:-

Radius:- 8 cm

Height:- 21 cm

Volume:- πr²h

22÷7×8×8×21

4224 cu.cm

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Answer 2

${\underline{\underline{\bf{Question\:1:}}}}$

• Find the total surface area of a right-circular cylinder whose base radius is 7 cm and height is 8 cm.

${\underline{\underline{\bf{Answer:}}}}$

• The total surface area is 660 cm².

${\underline{\underline{\bf{Explanation:}}}}$

Given:

• Base radius of a cylinder = 7 cm.
• Height of the cylinder = 8 cm.

Need to find:

• The Total Surface Area (TSA) of the cylinder.

Formula to be used:

$\small\underline{\boxed{\sf{{TSA}_{(Cylinder)}=2\pi r (h+r)\:sq.units}}}$

Solution:

By substituting the given measures in the formula,

$\:\:\:\:\:\:\:\:\:\implies{\sf{2\pi r (h+r)\:sq.units\:\:\:\:\:\:\:(\pi=\frac{22}{7})}}$

$\:\:\:\:\:\:\:\:\:\implies{\sf{2\times \frac{22}{\cancel{7}}\times \cancel{7}\times (8+7)}}$

$\:\:\:\:\:\:\:\:\:\implies{\sf{2\times 22\times 15}}$

$\:\:\:\:\:\:\:\:\:\implies{\sf{44\times 15}}$

$\:\:\:\:\:\:\:\:\:\implies{\boxed{\sf{\red{660\:{cm}^{2}}}}}$

• Hence, the TSA of the right-circular cylinder is 660 cm².

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${\underline{\underline{\bf{Question\:2:}}}}$

• Find the volume of a cylinderical can of height 21 cm and base radius 8 cm.

${\underline{\underline{\bf{Answer:}}}}$

• The volume is 4224 cm³.

${\underline{\underline{\bf{Explanation:}}}}$

Given:

• Height of a cylinderical can = 21 cm.
• Base radius of the cylinderical can = 8 cm.

Need to find:

• The volume of the cylinderical can.

Formula to be used:

$\small\underline{\boxed{\sf{{Volume}_{(Cylinder)}=\pi {r}^{2}h\:cu.units}}}$

Solution:

By substituting the given measures in the formula,

$\:\:\:\:\:\:\:\:\:\implies{\sf{\pi {r}^{2}h\:cu.units\:\:\:\:\:\:\:(\pi=\frac{22}{7})}}$

$\:\:\:\:\:\:\:\:\:\implies{\sf{\frac{22}{\cancel{7}}\times {8}^{2}\times {\cancel{21}}^{3}}}$

$\:\:\:\:\:\:\:\:\:\implies{\sf{22\times 8\times 8\times 3}}$

$\:\:\:\:\:\:\:\:\:\implies{\sf{176\times 24}}$

$\:\:\:\:\:\:\:\:\:\implies{\boxed{\sf{\red{4224\:{cm}^{3}}}}}$

• Hence, the volume of the cylinderical can is 4224 cm³.

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