Question

A rectangular tank 1.5 m long, 1.2 m broad and 1.8 m deep ia half full of water. If a brick absorbs 1/15 of its own volume of water. How many bricks 15 cm long, 6 cm broad and 5 cm thick must be put into tank so that water may reach to the top of the tank.​

Answer 1

3857 ⅐ bricks

Step-by-step explanation:

$\blue{ \bigstar{ \textsf{ \textbf{Given:- }}}}$

• A rectangular tank 1.5 m long, 1.2 m broad and 1.8 m deep ia half full of water. If a brick absorbs 1/15 of its own volume of water.

$\blue{ \bigstar \textsf{ \textbf{To\:Find:- }}}$

• Bricks 15 cm long, 6 cm broad and 5 cm thick must be put into tank so that water may reach to the top of the tank.

$\blue{ \bigstar{ \textsf{ \textbf{Solution:-}}}}$

$\begin{gathered} \sf \: Volume \: of \: water \: in \: the \: tank \\ \\ \longmapsto \: \sf \pink{ \frac{1}{2} \times l \times b \times h \: ( as \: it \: is \: half \: full) }\\ \\ \\ \longmapsto \sf \: \frac{1}{2} \times 150 \times 120 \times 180 \\ \\ \\ \red{\longmapsto \sf \: {1620000 {cm}^{3} }} \\ \\ \\ \\ \green\bigstar \sf \: Let \: the \: number \: of \: bricks \: required \: be \: x \\ \\ \\ \sf \: Volume \: of \: x \: bricks \\ \\ \\ \leadsto \: \sf \pink{\: l \times b \times h \times x} \\ \\ \\ \leadsto \: 15 \sf \: \times 6 \times 5 \times x \\ \\ \\ \leadsto \sf \: 450x \: {cm}^{3} \\ \\ \\ \\ \sf \: Volume \: of \: water \: absorbed \\ \\ \\ \dashrightarrow \: \sf \cancel{\frac{1}{15} \times 450x} \\ \\ \\ \dashrightarrow \sf \: 30x \: {cm}^{3} \\ \\ \\ \\ \sf\large{ \clubs \: ACQ} \\ \\ \\ \therefore \: \tt 450x - 30x = 1620000 \\ \\ \\ \longrightarrow \tt \: 420x = 1620000 \\ \\ \\ \longrightarrow \tt \: x = \cancel\frac{1620000}{420} \\ \\ \\ \longrightarrow \tt \: x = \frac{81000}{21} \\ \\ \\ \longrightarrow \underline \red{\boxed{ \bigstar \: \frak{x = 3857 \frac{1}{7}}}} \\ \\ \\ \\ \underline{ \bf \therefore \: \bigstar \: Required \: number \: of \: bricks = 3857 \frac{1}{7} }\end{gathered}$