Question

From a solid metallic cylinder of height 24cm, a cone of same height and same base (as cylinder) is taken out. the density of the metal is 10gm per cm^3. if the mass of the remaining portion of the cylinder is 24.64 kg, then find the cost required to paint the remaining portion at a rate of rs 3 per 440 cm^2.​

Answer 1

$\red{\textbf{Rs .12}}$

Step-by-step explanation:

$volume \: of \: remaining \: part \: of \: solid =$

$\pi {r}^{2} h -\Large \frac{1}{3} \small\pi {r}^{2} h$

$= \Large \frac{2}{ 3} \pi {r}^{2} h$

$density \: is \: given \: as \: 10gm | {cm}^{3}$

$mass \: of \: every \: 1 {cm}^{3} = 10gms$

$it \: is \: given \: that$

$mass \: of \: remaining \: portion = 24.64kg$

$= 24640gms$

$then$

$\Large\frac{2}{3} \times \frac{22}{7} \times {r}^{2} \times 24 \times 10$

$= 24640$

${r}^{2} = 49$

$r = 7$

$slant \: height \: of \: cone \: =$

$\sqrt{( {24})^{2} +( {7})^{2} }$

$\sqrt{625} = 25$

$surface \: area \: of \: remaining \: area \: =$

$2\pi \: rh + \pi {r}^{2} + \pi \: rl$

$= \pi \times r(2h + r + l)$

$= 22 \times 7 /7 (2 \times 24 + 7 + 25)$

$= 22(48 + 32)$

$= 22(80)$

$= 1760 {cm}^{2}$

$cost \: of \: painting \: per \: 440 {cm}^{2} = 3$

$cost \: of \: painting \: 1760 {cm}^{2} =$

$1760 \times \Large \frac{3}{440}$

$= 4 \times 3 = 12$

$\red{\textbf{so, the cost is Rs.12}}$

Answer 2

Answer:

Step-by-step explanation:

volume \: of \: remaining \: part \: of \: solid =volumeofremainingpartofsolid=

\pi {r}^{2} h -\Large \frac{1}{3} \small\pi {r}^{2} hπr2h−31πr2h

= \Large \frac{2}{ 3} \pi {r}^{2} h=32πr2h

density \: is \: given \: as \: 10gm | {cm}^{3}densityisgivenas10gm∣cm3

mass \: of \: every \: 1 {cm}^{3} = 10gmsmassofevery1cm3=10gms

it \: is \: given \: thatitisgiventhat

mass \: of \: remaining \: portion = 24.64kgmassofremainingportion=24.64kg

= 24640gms=24640gms

thenthen

\Large\frac{2}{3} \times \frac{22}{7} \times {r}^{2} \times 24 \times 1032×722×r2×24×10

= 24640=24640

{r}^{2} = 49r2=49

r = 7r=7

slant \: height \: of \: cone \: =slantheightofcone=

\sqrt{( {24})^{2} +( {7})^{2} }(24)2+(7)2

\sqrt{625} = 25625=25

surface \: area \: of \: remaining \: area \: =surfaceareaofremainingarea=

2\pi \: rh + \pi {r}^{2} + \pi \: rl2πrh+πr2+πrl

= \pi \times r(2h + r + l)=π×r(2h+r+l)

= 22 \times 7 /7 (2 \times 24 + 7 + 25)=22×7/7(2×24+7+25)

= 22(48 + 32)=22(48+32)

= 22(80)=22(80)

= 1760 {cm}^{2}=1760cm2

cost \: of \: painting \: per \: 440 {cm}^{2} = 3costofpaintingper440cm2=3

cost \: of \: painting \: 1760 {cm}^{2} =costofpainting1760cm2=

1760 \times \Large \frac{3}{440}1760×4403

= 4 \times 3 = 12=4×3=12

\red{\textbf{so, the cost is Rs.12}}so, the cost is Rs.12