Question

the curved surface area of a powder can is 879.2 sq.cm and the diameter of the base is 28 cm.Find the height and volume of the can​

Answer 1

• Height of cane is 9.99 cm.
• Volume of cane is 6153.84 cm³.

Step-by-step explanation:

Given:-

• Curved surface area of a powder cane is 879.3 cm².
• Diameter of the base is 28 cm.

To find:-

• Height of cane.
• Volume of cane.

Solution:-

Radius = Diameter/2

= 28/2

= 14

Radius of cane is 14 cm.

Let, Height of cane be h.

• We know the shape of cane is cylinder.

$\boxed{\sf \bold{Curved \: surface \: area \: of \: cylinder = 2 \pi r h}}$

Where,

• r is radius and h is height of cylinder.

Put r, h and curved surface area in formula :

$\sf \longrightarrow 879.2 = 2\times \dfrac{22}{\cancel{7}} \times \cancel{14} \times h$

$\sf \longrightarrow 879.2 = 44 \times 2 \times h$

$\sf \longrightarrow 879.2 = 88 \times h$

$\sf \longrightarrow h = \dfrac{879.2}{88}$

$\longrightarrow \purple{ \boxed{\sf \bold{h = 9.99}}\star}$

Height of cane is 9.99 cm.

$\boxed{\sf \bold{Volume \: of \: cylinder = \pi r^{2} h}}$

Put r and h in formula :

$\sf \longrightarrow \dfrac{22}{7} \times (14)^{2} \times 9.99$

$\sf \longrightarrow \dfrac{22}{\cancel{7}} \times \cancel{14} \times 14 \times 9.99$

$\sf \longrightarrow 22 \times 2 \times 14 \times 9.99$

$\sf \longrightarrow 44 \times 14 \times 9.99$

$\longrightarrow \red{\boxed{\sf \bold{6153.84}}\star}$

Therefore,

Volume of cane is 6153.84 cm³.

Answer 2

$\rule{200}4$

$\underline{\underline{\sf{ \color{red}{\qquad Given\:: \qquad} }}}$

• Curved surface area of cylindrical powder cane is 879.2 cm².

• It's base diameter is 28 cm.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

• ∴ Radius = $\sf{\dfrac{D}{2}}$ = $\sf{\dfrac{28}{2}}$ = $\sf{\cancel{\dfrac{28}{2}}}$ = 14 cm.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\underline{\sf{ \color{red}{\qquad To\:Find\:: \qquad} }}}$

• Height and volume of cane.

$\underline{\underline{\sf{ \color{red}{\qquad Diagram\:: \qquad} }}}$

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{14\ cm}}\put(9,17.5){\sf{?}}\end{picture}$

$\underline{\underline{\sf{ \color{red}{\qquad Solution\:: \qquad} }}}$

As we know that :-

${\red\bigstar\:\underline{\boxed {\bold \green {Curved\:surface\:area(CSA)_{(Cylinder)}\:=\:2\pi rh}}}}$

Putting all values :-

$\ratio\longrightarrow$ $\sf\:\:\:{2\:\times\:\dfrac{22}{7}\:\times\:14\:\times\:h\:=\:879.2}$

$\ratio\longrightarrow$ $\sf\:\:\:{2\:\times\:\dfrac{22}{\cancel{7}}\:\times\:\cancel{14}\:\times\:h\:=\:879.2}$

$\ratio\longrightarrow$ $\sf\:\:\:{2\:\times\:22\:\times\:2\:\times\:h\:=\:879.2}$

$\ratio\longrightarrow$ $\sf\:\:\:{88\:\times\:h\:=\:879.2}$

$\ratio\longrightarrow$ $\sf\:\:\:{h\:=\:\dfrac{879.2}{88}}$

$\ratio\longrightarrow$ $\sf\:\:\:{h\:=\:\cancel{\dfrac{879.2}{88}}}$

$\ratio\longrightarrow$ $\:\:\:\underline{\sf{h\:=\:9.99}}$

$\underline{\boxed {\frak {\therefore \red {Height_{(Cylindrical\:cane)}\:\leadsto\:9.99\:cm}}}}\:\blue\bigstar$

Now,

${\red\bigstar\:\underline{\boxed {\bold \green {Volume_{(Cylinder)}\:=\:\pi r^2h}}}}$

Putting all values :-

$\ratio\implies$ $\sf{\dfrac{22}{7}\:\times\:(14)^2\:\times\:9.99}$

$\ratio\implies$ $\sf{\dfrac{22}{7}\:\times\:14\:\times\:14\:\times\:9.99}$

$\ratio\implies$ $\sf{\dfrac{22}{\cancel{7}}\:\times\:\cancel{14}\:\times\:14\:\times\:9.99}$

$\ratio\implies$ $\sf{22\:\times\:2\:\times\:14\:\times\:9.99}$

$\ratio\implies$ $\underline{\sf{6153.84}}$

$\underline{\boxed {\frak {\therefore \red {Volume_{(Cylindrical\:cane)}\:\leadsto\:6153.84\:cm^3}}}}\:\blue\bigstar$

NOTE :-

• Dear user if you are not able to see the diagram from app. Please see it from the the site (brainly.in). It will be correctly displayed there.

$\rule{200}4$