Question

9. The height of a cylinder whose radius is 7 cm and the total surface area is 968 cm2 is:

A. 15 cm

B. 17 cm

C. 19 cm

D. 21 cm

​

Answer 1

Given total surface area of Cylinder is 968cm²

And, The radius of cylinder is 7 cm

⠀⠀⠀⠀⠀⠀⠀

We have to find height of cylinder.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

☯ Let height of cylinder be h.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\underline{\bigstar\:\boldsymbol{According\:to\: Question\::}}$

⠀⠀⠀⠀⠀⠀⠀

☯ Total surface area of Cylinder is 968cm²

⠀⠀⠀⠀⠀⠀

⋆ Reference of image is shown in diagram

⠀⠀⠀⠀⠀⠀

$\setlength{\unitlength}{1 mm}\begin{picture}(5,5)\qbezier(2,3)(8,8)(14,3)\qbezier(2,3)(8,-4)(14,3)\put(2,-27){\line(0,2){30}}\put(14,-27){\line(0,2){30}}\qbezier(2,-27)(8,-35)(14,-27)\qbezier(2,-27)(8,-20)(14,-27)\put(8,-27){\line(0,2){30}}\put(9,-14){ \tt{h} }\put(9,-29){ \tt{7 cm} }\put(8,-27){\line(2,0){6}}\put(8,3){\line(2,0){6}}\put(15,-14){ \tt{T.S.A. = 968cm^{2}} }\put(9,-34){ \tt{} }\end{picture}$

⠀⠀⠀⠀⠀⠀

$\dag\;{\underline{\frak{We\;know\;that\;:}}}$

⠀⠀⠀⠀⠀⠀⠀

$\star\;{\boxed{\sf{\purple{T.S.A.\;of\;cylinder = 2\pi r (r + h)}}}}$

⠀⠀⠀⠀⠀⠀⠀

$\dag\;{\underline{\frak{Putting\;values\;:}}}$

⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 44(7 + h) = 968$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 7 + h = \dfrac{968}{44}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 7 + h = \cancel{ \dfrac{968}{44}}$

⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀

$:\implies{\underline{\boxed{\sf{\purple{h = 15\;cm}}}}}\;\bigstar$

⠀⠀⠀⠀⠀⠀⠀

$\therefore$ Height of cylinder is 15 cm.

⠀⠀⠀⠀⠀⠀⠀

Hence, Option A is correct.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

★ More to know:

⠀⠀⠀⠀⠀⠀⠀

• C.S.A. of Cylinder = 2πrh

• Volume of Cylinder = πr²h

• Area of base of Cylinder = πr²

Answer 2

$\sf\huge\underline{Explanation :-}$

Given :

• Radius of the cylinder = 7 cm.
• Total surface area of the cylinder = 968 cm²

To find :

• The height of the cylinder.

Solution :

In the given question, the radius and total surface area of the cylinder is given. We've to find the height.

Let the height of the cylinder be 'h'

We know that,

Total surface area of cylinder = 2πr(h + r) sq.unit

According to question,

$\sf\longrightarrow 2\pi \: r(h \: + r) = 968$

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

$\sf\longrightarrow 2 \times 22 (h + 7) = 968$

$\sf\longrightarrow 44 (h + 7) = 968$

$\sf\longrightarrow (h + 7) = \dfrac{968}{44}$

$\sf\longrightarrow h + 7 = 22$

$\sf\longrightarrow h = 22 - 7$

$\sf\therefore h = 15$

Hence, the height of the cylinder is 15 cm.

Therefore, the correct option is -

$\sf\huge\boxed{a) \: 15 \: cm}$

$\bf\huge\underline{More \: formulas :-}$

• Volume of cylinder = πr²h [where π = 22/7, r = radius & h = height.] cu.unit
• Total surface area of sphere = 4πr² sq.unit
• Volume of sphere = 4/3 × πr³ cu.unit