Question

Answer pls with explanation

Answer 1

Answer:

Question :-

• Find the height of a cylinder whose diameter is 14 cm and total surface area is 968 cm².

Given :-

• A cylinder whose diameter is 14 cm and total surface area is 968 cm².

To Find :-

• What is the height of a cylinder.

Formula Used :-

$\clubsuit$ Radius Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Radius =\: \dfrac{Diameter}{2}}}}\: \: \: \bigstar$

$\clubsuit$ Total Surface Area Of Cylinder Formula :

$\small \bigstar \: \: \sf\boxed{\bold{\pink{Total\: Surface\: Area_{(Cylinder)} =\: 2{\pi}r(r + h)}}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius
• h = Height

Solution :-

First, we have to find the radius of a cylinder :

Given :

• Diameter = 14 cm

According to the question by using the formula we get,

$\implies \bf Radius =\: \dfrac{Diameter}{2}$

$\implies \sf Radius =\: \dfrac{14}{2}$

$\implies \sf\bold{\blue{Radius =\: 7\: cm}}$

Hence, the radius is 7 cm .

Now, we have to find the height of a cylinder :

Given :

• Radius = 7 cm
• Total Surface Area = 968 cm²

According to the question by using the formula we get,

$\small \implies \bf Total\: Surface\: Area_{(Cylinder)} =\: 2{\pi}r(r + h)$

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

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

$\implies \sf 968 =\: \dfrac{308}{7} \times (7 + h)$

$\implies \sf 968 \times \dfrac{7}{308} =\: 7 + h$

$\implies \sf \dfrac{6776}{308} =\: 7 + h$

$\implies \sf 22 - 7 =\: h$

$\implies \sf 15 =\: h$

$\implies \sf\bold{\red{h =\: 15\: cm}}$

$\sf\bold{\purple{\underline{\therefore\: The\: height\: of\: a\: cylinder\: is\: 15\: cm\: .}}}$