Question

Find the height of the cylinder of radius 3.5cm and the total surface area is 968cm square.​

Answer 1

Answer:

40.52 cm ----- This is the answer

Answer 2

Answer:

Given :-

• A cylinder whose radius is 3.5 cm and the total surface area is 968 cm².

To Find :-

• What is the height of the cylinder.

Formula Used :-

$\clubsuit$ Total Surface Area or T.S.A of Cylinder Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{T.S.A_{(Cylinder)} =\: 2{\pi}r(r + h)}}}\: \: \: \bigstar$

where,

• T.S.A = Total Surface Area
• π = Pie or 22/7
• r = Radius
• h = Height

Solution :-

Let,

$\mapsto \bf Height_{(Cylinder)} =\: h\: cm$

Given :

• Radius (r) = 3.5 cm
• Total surface area (T.S.A) = 968 cm²

According to the question by using the formula we get,

$\implies \bf T.S.A_{(Cylinder)} =\: 2{\pi}r(r + h)$

$\implies \sf 968 =\: 2 \times \dfrac{22}{7} \times 3.5(3.5 + h)$

$\implies \sf 968 =\: \dfrac{44}{7} \times 3.5(3.5 + h)$

$\implies \sf 968 =\: \dfrac{154}{7} \times (3.5 + h)$

$\implies \sf 968 \times \dfrac{7}{154} =\: 3.5 + h$

$\implies \sf \dfrac{6776}{154} =\: 3.5 + h$

$\implies \sf 44 =\: 3.5 + h$

$\implies \sf 44 - 3.5 =\: h$

$\implies \sf 40.5 =\: h$

$\implies \sf\bold{\red{h =\: 40.5\: cm}}$

$\therefore$ The height of the cylinder is 40.5 cm .