Question

Find the total surface area of right circular cylinder whose base area is346.5cm^2 and whose height is 24cm ​

Answer 1

Given:

• Base area of a right circular cylinder is 346.5cm²

• The hieght of the cylinder is 24cm

To Find:

• the total surface area of the cylinder

Daiagram:

$\setlength{\unitlength}5cm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{10.5\: cm}}\put(9,17.5){\sf{24\: cm}}\end{picture}$

Solution:

◐ Now, here we have got the base of the cylinder and the height of the and its said to find the total surface area of it.

${\underline{\pink{\mathfrak{As\: we\: know\:that:}}}}$

$\longrightarrow\blue{ \underline{ \boxed{ \pink{ \mathfrak{ t.s.a \: of \: a \: cylinder = 2\pi \: r(r + h)}}}}\bigstar}$

─────────────────────────────────

» hieght = 24cm

» radius = ?

➛so, we need to find the radius of the cylinder to find its total surface area.

➢ as, the area of the base is given let's find the radius with the help of it.

${\underline{\pink{\mathfrak{As\: we\: know\:that:}}}}$

$\longrightarrow\blue{ \underline{ \boxed{ \pink{ \mathfrak{area \: of \: the \: base = \pi \: {r}^{2} }}}} \bigstar}$

➜ now, let's substitute the values and find the value of the radius

$\longrightarrow \sf \: 346.5 {cm}^{2} = \pi {r}^{2} \\ \\ \\ \longrightarrow \sf 346.5 = \frac{22}{7} \times \: {r}^{2} \\ \\ \\ \longrightarrow \sf {r}^{2} = \frac{346.5 \times 7}{22} \: \: \: \\ \\ \\ \longrightarrow \sf {r}^{2} = 110.25 \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: r = \sqrt{110.25} \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \orange{ r = 10.5 \bigstar} \: \: \: \: \: \: \: \: \: \:$

↝so, the radius equals 10.5cm

❍ Now, let's substitute the values and find the total surface area of the cylinder .

${ : \implies} \sf \: t.s.a = 2 \pi {r}^{2} + 2\pi \: rh \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf \: t.s.a = 2\pi \: r(r + h) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf \: t.s.a = 2 \times \frac{22}{7} \times 10.5(10.5 + 24) \\ \\ \\ \\ { : \implies} \sf \: t.s.a = 66 \times (34.5) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ { : \implies} \sf \pink{ t.s.a =} \blue{ \underline{ \boxed{ \pink{ \mathfrak{ 2277 {cm}^{2} }}}} \bigstar}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

➺the total surface area is 2277cm²

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

note: app user ? kindly see ot from the web for the diagram

Answer 2

Answer :

• Total surface area of right circular cylinder is 2277cm²

Given :

• base area is 346.5cm²
• height is 24cm

To find :

• Total surface area of right circular cylinder

Solution :

As we know that :

• Area of base = πr²

Given that ,

base area is 346.5cm²

Then,

⟾ 22/7 × r² = 346.5cm

⟾ r² = 346.5 × 7/22

⟾ r² = 110.25

⟾ r² = √110.25

⟾ r = 10.5cm

so,Radius is 10.5cm

Now we have to find the total surface area of right circular cylinder

As we know that

• Total surface area of right circular cylinder = 2πrh + 2πr²

⟾ 2 × 22/7 × 10.5 × 24 + 2 × 22/7 × 10.5 × 10.5

⟾ 1584 + 693

⟾ 2277 cm²

Hence , total surface area of right circular cylinder is 2277cm²