Question

Mensuration: Cylinder and Sphere
2.
a)
find its total surface area.
a)
If the circumference of the circular base of a cylinder with height 20 cm
cylinder is 88 cm​

Answer 1

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

If the circumference of the circular base of a cylinder with height 20 cm is 88 cm , find its total surface area .

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

Total Surface Area of Cylinder = 2992 $\sf {cm}^{2}$

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

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

• Circumference of the circular base of a cylinder = 88 cm

• Height of cylinder = 20 cm

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

• Total Surface Area of Cylinder .

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

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

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

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

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

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

$\displaystyle \longrightarrow \textsf{TSA of cylinder } \sf = 2 \times \frac{22}{ \cancel7} \times \cancel{14} { \: }^{2} (20 + 14) \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{TSA of cylinder } \sf =2 \times 22 \times 2 \times 34 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \textsf{TSA of cylinder } \sf =2992 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{ \boxed{ \begin{array}{l} \textsf{TSA of cylinder = \sf2992 \: {cm}^{2} } \end{array}}}$