Question

3 no. the volume of the cyclinder is 448π cm and height 7 cm. find its lateral curved surface and total curve surface​

Answer 1

Step-by-step explanation:

Let the radius be r

so

$\pi {r}^{2}h \: = 448\pi$

$\pi {r}^{2} \times 7 = 448\pi$

${r}^{2} = 64$

$r \: = \: 8$

Area of the lateral surface = 2 × 22/7 × 8 × 7

= 192 cm^2

Total surface Area = 192 + 2 × 22/7 × 8²

= 192 + 402.29

= 594.29 cm^2

Answer 2

$\huge\bf\red{Question : - }$

• The volume of a cylinder is 448π cm³ and Height 7cm. Find it's Lateral ( curved ) surface area and total surface area

Given :-

• Volume of the Cylinder is 448π cm³

• Height of the Cylinder is 7cm

To Find :-

• Lateral surface area of the Cylinder

• Total surface area of the Cylinder

Solution :-

➻ Let the radius and height of the cylinder be ' r ' cm and ' h ' cm

Now, Volume = 448π cm³

As we know that,

⠀⠀$\large\boxed{\sf{\purple{volume_{(cylinder)} = \pi {r}^{2}h }}}$

$\begin{gathered}:\implies\ πr²h = 448 cm³\\\\:\implies\sf r² × 7 = 448 ( height = 7cm)\\\\:\implies\sf r² = \frac{448}{7}\\\\:\implies\sf r² = 64 \\\\:\implies\sf r = √64\\\\:\implies{\underline{\boxed{\bf{\pink{ r = 8cm }}}}}\end{gathered}$

Hence ,The Radius of the base of cylinder is 8cm

By using formula,

⠀⠀⠀$\large\boxed{\sf{\purple{lateral \: surface \: area \: = 2\pi rh}}}$

By substituting values,

⠀⠀$\begin{gathered}:\implies\sf 2 × \frac{22}{\cancel7} × 8 ×\cancel 7\\\\:\implies\sf (2 \times 22 \times 8) {cm}^{2} \\\\:\implies{\underline{\boxed{\bf{\pink{352 {cm}^{2} }}}}}\end{gathered}$

Hence, The lateral surface area of the Cylinder is 352cm²

Now,

⠀⠀⠀$\large\boxed{\sf{\purple{Total \: surface \: area \: = 2πr( r + h )}}}$

By substituting values,

$\begin{gathered}:\implies\sf 2 × \frac{22}{7} × 8 ( 8 + 7 ) \\\\:\implies\sf 2 × \frac{22}{7} × 8 ( 15 ) \\\\:\implies\sf \frac{5280}{7} \\\\:\implies{\underline{\boxed{\bf{\pink{754.28 cm² ( approx )}}}}}\end{gathered}$

Hence, The Total surface area of the Cylinder is 754.28cm²