Question

the circumference of a base of a cylinder is 88 cm and its height is 14cm find the total surface area of the cylinder​

Answer 1

Answer:

2,464 cm²

Explanation:

We have, Circumference of base of cylinder = 88 cm

Height of cylinder = 14 cm

By using the formula,

Circumference of base of cylinder = 2πr

So,

2πr = 88

2 × 22/7 × r = 88

r = 88×7 / 44

= 616/44

= 14cm

Radius of cylinder = 14 cm

∴ Total surface area area of cylinder = 2πr (h+r) = 2 × 22/7 × 14 (14 + 14)

= 2 × 22/7 × 14 × 28

= 2,464 cm²

Answer 2

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

The circumference of a base of a cylinder is 88 cm and its height is 14 cm . Find the total surface area of the cylinder .

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

Total Surface Area of Cylinder = 2464 $\sf {cm}^{2}$

$\huge\purple{ \underline{ \boxed{\mathbb{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

Circumference of the circular base of a cylinder = 88 cm

Height of cylinder = 14 cm

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

Total Surface Area of Cylinder .

$\green{ \large \underline{ \mathbb{\underline{FORMULAS \: USED: }}}}$

$\purple{ \boxed{ \begin{array}{l} \textsf{Circumference of circle = 2\pi \sf r } \\ \\\textsf{TSA of cylinder = 2\pi \sf r(h + r) } \end{array}}}$

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

$\textsf{Circumference of circular base of cylinder} = \sf2\pi r \\ \\ \displaystyle \sf \longrightarrow88 = 2 \times \frac{22}{7} \times r \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow88 = \frac{44}{7} \times r \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow r = \frac{ \cancel{88} { \: }^{2} \times 7}{ \cancel{44}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow r = 14 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{ \boxed{ \textsf{Radius of cylinder = 14 cm}}}$

$\red{ \underline{\underline{ \textsf{TSA of cylinder : }}}}$

$\displaystyle \longrightarrow \textsf{TSA of cylinder } \sf = 2 \times \frac{22}{ \cancel7} \times \cancel{14} { \: }^{2} (14+ 14) \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{TSA of cylinder } \sf =2 \times 22 \times 2 \times 28 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{TSA of cylinder } \sf =2464 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{ \boxed{ \begin{array}{l} \textsf{TSA of cylinder = \sf2464 \: {cm}^{2} } \end{array}}}$