Question

The size of a plant cell is 0.00001275 m and that of a red blood cell is 0.000007 m. Show that the plant cell is twice the size of a red blood cell.

Answer 1

SOLUTION -

$\frac{size \: of \: plant \: cell}{size \: of \: red \: blood \: cell} = \frac{0.00001275m}{0.000007m}$

$⟹\frac{size \: of \: plant \: cell}{size \: of \: red \: blood \: cell} = \frac{ \frac{1275}{10 ^{8}m } }{ \frac{7}{ {10}^{26}m } }$

$⟹ \frac{size \: of \: plant \: cell}{size \: of \: red \: blood \: cell} = \frac{1275 \times {10}^{ - 8} }{7 \times {10}^{ - 6} }$

$⟹ \frac{size \: of \: plant \: cell}{size \: of \: red \: blood \: cell} = \frac{12.75 \times {10}^{ 2} \times 10^{ - 8} }{7 \times {10}^{ - 6} }$

$⟹\frac{size \: of \: plant \: cell}{size \: of \: red \: blood \: cell} = \frac{12.75 \times {10}^{ - 6} }{7 \times {10}^{ - 6} }$

$≈ \frac{13}{7} (approx.)$

$= \frac{2}{1} (approx.)$

→ size of plant cell = 2 × size of red blood cell

★hence , the size of plant cell is twice the size of red blood cell.

Answer 2

$\sf\Large{\underbrace{\red{Answer \implies 1:2\: (approx.)}}}$

$\sf\large{\underline{\underline{Given:}}}$

$\sf{The\:size\:of\:red\:blood\:cell = 0.000007\:m = 7 \times {10}^{-6}\:m}$

$\sf{and,}$

$\sf{the\:size\:of\:plant\:cell = 0.00001275\:m = 1.275 \times {10}^{-5}\:m }$

$\sf\large{\underline{\underline{Now,}}}$

$\sf{The\:approximate\:ratio\:of\:their\:size = \dfrac{(7 \times {10}^{-6})}{(1.275 \times {10}^{-5})}}$

$\sf{ = \dfrac{(7 \times {10}^{-6+5})}{1.275} \: \: \: \: ..........\: \: \: (\dfrac{{a}^{m}}{{a}^{n}} = {a}^{m -n})}$

$\sf{ = \dfrac{(7 \times {10}^{-1})}{1.275}}$

$\sf{ = \dfrac{(7 \times \dfrac{1}{10})}{1.275}}$

$\sf{ = \dfrac{(\dfrac{7}{10})}{1.275}}$

$\sf{ = \dfrac{0.7}{1.3} \: \: \:........... \: \: \: \: (1.275 = 1.3)}$

$\sf{ = \dfrac{7}{13}}$

$\sf{ = \dfrac{1}{2}............(approx.)}$

$\bold{\fbox{\color{red}{So,\: the\:approximate\:ratio\:of\:their\:size = 1 : 2}}}$