Question

1. The circumference of the base of a right circular cylinder is 44 cm. If its whole surface
area is 968 cm2 then the sum of its height and radius is
a. 18 cm
b. 22 cm.
C. 20 cm.
d. 16 cm.​

Answer 1

Given :-

• Circumference of the base of the cylinder = 44 cm
• Total surface area of the cylinder = 968 cm²

To Find :-

• Sum of height and radius of the cylinder ?

Solution :-

we know that,

if ‘r’ is the radius of base of the cylinder, then

$\boxed{ \bold{circumference \: of \: base = 2\pi r}}$

$\bold{: \implies2\pi r = 44 \: cm } \: \: \: \:....(i)$

and now,

if ‘r’ and ‘h’ are the radius and height of the cylinder respectively, then

$\boxed{ \bold{T.S.A \: of \: cylinder = 2\pi r(r + h)}}$

$\bold{: \implies2\pi r(r + h) =968 }$

now, put the value of 2πr from (i)

$\bold{: \implies 44(r + h) = 968} \\ \\ \bold{: \implies r + h = \frac{968}{44} } \: \: \: \: \: \: \: \\ \\ \bold{ : \implies r + h =22 \: } \: \: \: \: \: \: \: \: \:$

so, sum of height and radius of the cylinder is 22 cm

hence, option (b) is Correct

Answer 2

$\underline\purple{\bold{Given \: Question :- }}$

• The circumference of the base of a right circular cylinder is 44 cm. If its whole surface area is 968 cm^2, then the sum of its height and radius is

$\large \red{AηsωeR } ✍$

$\underline\blue{\bold{Given- }}$

• The circumference of the base of a right circular cylinder is 44 cm.
• The whole surface area is 968 cm^2.

$\underline\blue{\bold{To \: Find }}$

• The sum of its height and radius.

$\underline\blue{\bold{Formula \: Used : }}$

${{ \boxed{{\bold\green{Total \: Surface \: Area_{(Cylinder)}\: = \:2\pi r(h +r)}}}}}$

${{ \boxed{{\bold\purple{Circumference \: of \: base{(Cylinder)}\: = \:2\pi r}}}}}$

where,

• r = radius of cylinder
• h = height of cylinder

$\begin{gathered}\Large{\underline{\bf{\color{purple}CaLcUlAtIoN,}}} \end{gathered}$

$\begin{gathered}\begin{gathered}\bf Let = \begin{cases} &\sf{r \: be \: the \: radius \: of \: cylinder} \\ &\sf{h \: be \: the \: height \: of \: cylinder} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\bf\red{According \: to \: statement}\end{gathered}$

⟼ The circumference of the base of a right circular cylinder is 44 cm.

$\sf \: ⟼2\pi \: r = 44 \: ⟼ \: (1)$

$\begin{gathered}\bf\pink{According \: to \: statement}\end{gathered}$

⟼ The whole surface area of cylinder is 968 cm^2.

$\sf \: ⟼2\pi \: r(h + r) = 968$

⟼ On substituting the value from equation (1), we get

$\sf \: ⟼44 \times (h + r) = 968$

$\sf \: ⟼h + r = \dfrac{968}{44}$

$\sf \: ⟼ \: h + r = 22 \: cm$

$\large{\boxed{\boxed{\bf{Option \: (b) \: is \: correct}}}}$

___________________________________________

☆ More info:

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length)²+(breadth)²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²