Question

the volume of a soap cake is 160cm3 its length and width are called as a 10 cm and 5 cm Find the height

With explanation pls

Answer 1

$\normalsize{\underline{\underline{\bf{Given:}}}}$

$\:\:\:\normalsize\bullet{\sf{Volume\:of\:a\:soap\:cake\:is\:160\:{cm}^{3}.}}$

$\:\:\:\normalsize\bullet{\sf{Length\: of\:the\:soap\:cake\:is\:10\:cm.}}$

$\:\:\:\normalsize\bullet{\sf{Width\:(breadth)\: of\:the\:soap\:cake\:is\:5\:cm.}}$

$\normalsize{\underline{\underline{\bf{Need\:to\:find:}}}}$

$\:\:\:\normalsize\bullet{\sf{The\:height\:of\:the\:soap\:cake.}}$

$\normalsize{\underline{\underline{\bf{Formula\:to\:be\:used:}}}}$

$\:\:\:\normalsize\bullet\underline{\boxed{\sf{{Volume}_{(cuboid)}= L\times B\times H\:cu.units}}}$

$\normalsize{\sf{Where,}}$

• $\normalsize{\sf{L=Length}}$
• $\normalsize{\sf{B=Breadth}}$
• $\normalsize{\sf{H=Height}}$

$\normalsize{\underline{\underline{\bf{Solution:}}}}$

$\normalsize{\sf{Substituting\:the\: given\:measures\:in\:the\:formula,}}$

$\:\:\:\:\:\:\:\:\normalsize\longrightarrow{\sf{160=10\times 5\times H}}$

$\:\:\:\:\:\:\:\:\normalsize\longrightarrow{\sf{160=50\times H}}$

$\:\:\:\:\:\:\:\:\normalsize\longrightarrow{\sf{H=\frac{16\cancel{0}}{5\cancel{0}}}}$

$\:\:\:\:\:\:\:\:\normalsize\longrightarrow{\sf{H=\frac{16}{5}=\red{\underline{3.2\:cm}}}}$

$\normalsize{\underline{\underline{\bf{Final\:answer:}}}}$

$\:\:\:\normalsize\bullet{\sf{The\:height\:of\:the\:soap\:cake\:is\:3.2\:cm.}}$

_______________________________________

$\normalsize{\underline{\underline{\bf{Related\:formulae:}}}}$

$\:\:\:\normalsize\bullet{\sf{{LSA}_{(cuboid)}=2\times H\times (L+B)\:sq.units}}$

$\:\:\:\normalsize\bullet{\sf{{TSA}_{(cuboid)}=2\times (LB+BH+HL)\:sq.units}}$