Question

The difference between outside and inside surfaces of a cylindrical metallic pipe 14 cm long is 44 cm². If pipe is made of 99 cm³ of metal, find the other and inner radii of the pipe.​

Answer 1

Step-by-step explanation:

$\blue{\mathfrak{\underline{\large{Given}}}:} \\length \: of \: cylinder = 14 \: cm \\volume \: of \: metal \: pipe = 99\: {cm}^{3} \\ difference \: between \: outer \: and \: inner \: surface \: area \\ = 44 \: {cm}^{2} \\ \blue{\mathfrak{\underline{\large{To \: find}}}:} \\ outer \: and \: inner \: radius =? \\\blue{\mathfrak{\underline{\large{Finding}}}:}\\ let \: area \: of \: outer \: surface = A_1 \: {cm}^{2} \\ outer \: radius = r_1\\ \: area \: of \: inner\: surface = A_2 \: {cm}^{2} \\ inner \: radius = r_2 \\ A_1-A_2 = 44 \: {cm}^{2} \\ 2\pi r_1h - 2\pi r_2h = 44 \\ 2\pi h(r_1-r_2) = 44 \\ 2 \times \frac{22}{7} \times 14 \times (r_1-r_2) = 44 \\ (r_1-r_2) = \frac{44 \times 7}{2 \times 22 \times 14} \\ (r_1-r_2) = 0.5 \: cm \\ r_1 - \frac{1}{2} = r_2 - (i) \\ volume \: of \: metal \: pipe = 99\: {cm}^{3} \\ circumference\:of \:circle\times l\times h = 99\\2\times \frac{22}{7} \times r_2 \times 14 \times \frac{1}{2}= 99 \\ 2\times \frac{22}{7} \times ( r_1 - \frac{1}{2}) \times 14 \times \frac{1}{2}= 99 \\ ( r_1-\frac{1}{2})= \frac{99 }{44} \\ ( r_1-\frac{1}{2}) = \frac{9}{4} \\ r_1 = \frac{9}{4} +\frac{1}{2} \\ r_1 = \frac{9+2}{4} =\frac{11}{4} \\ \blue{\boxed{ r_1 = 2.75\: cm}} \\ 2.75- \frac{1}{2} = r_2 \\ \blue{\boxed{ r_2 = 2.25 \: cm}} \\ \\ \red{\mathfrak{ \large{\underline{{Hope \: It \: Helps \: You}}}}} \\ \blue{\mathfrak{ \large{\underline{{Mark \: Me \: Brainliest}}}}}$