Question

the height of a right circular cylinder is 7 cm and radius 3cm find its curved surface area ,total surface area and volume​

Answer 1

Answer:

Given -

• Height, h = 7 cm
• Radius, r = 3 cm.

Let's find curved surface area of the cylinder -

$\\ \large{ \sf{ \underline{ \green{formula \: - \: 2\pi \: rh}}}} \\ \\ \\ \implies \sf \: 2 \times \frac{22}{7} \times 3 \times 7 \\ \\ \\ \implies \sf \: 6 \times 22 \\ \\ \\ \implies \sf \: 132 \: {cm}^{2}$

Total surface area of the cylinder -

$\\ \\ \large{ \sf{\underline{ \blue{formula - 2\pi \: r \: (r + h)}}}} \\ \\ \\ \implies \sf \: 2 \times \frac{22}{7} \times 3 \: (3 +7) \\ \\ \\ \implies \sf \: 60 \times \frac{22}{7} \\ \\ \\ \implies \sf \: 188.571 \: {cm}^{2}$

Volume of the cylinder -

$\\ \\ \large{ \sf \underline \orange{formula \: - \: \pi {r}^{2} h}} \\ \\ \\ \implies \sf \: \frac{22}{7} \times {3}^{2} \times 7 \\ \\ \\ \implies \sf \: 22 \times 3 \times 3 \\ \\ \\ \implies \sf \: 198 \: {cm}^{3}$

Hence,

• Total surface area = 188.57 cm²
• Curved surface area = 132 cm²
• Volume = 198 cm³

Answer 2

☢ Given :-

• Height of the cylinder (h) = 7 cm.

• Radius of base (r) = 3 cm.

$\underline{\bigstar\:\textbf{According to the Question :}}$

$\dashrightarrow\bf{\:\:CSA\:of\: cylinder = 2 \pi rh}\\\\\\\dashrightarrow\sf\:\: 2 \times \dfrac{22}{7}\times 3 \times 7\\\\\\\dashrightarrow\sf\:\: 22 \times 6 \\\\\\\dashrightarrow\:\:{\sf 132\:cm^2}$

$\therefore\:\underline{\textsf{CSA of cylinder is \textbf{132}} \:\sf{cm^3}}.$

$\rule{170}2$

$\dashrightarrow\bf{\:\:TSA\:of\: cylinder = 2 \pi r(h + r)}\\\\\\\dashrightarrow\sf\:\: 2 \times \dfrac{22}{7}\times 3 \: (7 + 3)\\\\\\\dashrightarrow\sf\:\: 2 \times \dfrac{22}{7} \times 3 \times 10 \\\\\\\dashrightarrow\sf\:\: \dfrac{1320}{7}\\\\\\\dashrightarrow\:\:{\sf 188.57\:cm^2}$

$\therefore\:\underline{\textsf{TSA of cylinder is \textbf{188.57}}\: \sf{cm^2}}.$

$\rule{170}2$

$\dashrightarrow\bf{\:\:Volume\:of\: cylinder = \pi r^2h}\\\\\\\dashrightarrow\sf\:\: \dfrac{22}{7}\times 3 \times 3 \times 7 \\\\\\\dashrightarrow\sf\:\: 22 \times 3 \times 3 \\\\\\\dashrightarrow\:\:{\sf 198\:cm^3}$

$\therefore\:\underline{\textsf{Volume of cylinder is \textbf{198}} \:\sf{cm^3}}.$