A cylindrical vessel of 40 cm radius is completely filled with...

Volume of the cylindrical vessel, $V = 528$ dm$^3 = 528000$ cm$^3$

Radius of the vessel, $r = 40$ cm

Let the height of the vessel be $H$.

$V = \pi r^2 H$

$528000 = \dfrac{22}{7} \times (40)^2 \times H$

$H = \dfrac{528000 \times 7}{22 \times 1600} = 105$ cm

The vessel is placed on a block of height equal to the vessel, so the height of the block is $105$ cm.

Depth of the hole from the top water level, $h = 70$ cm

Height of the hole from the ground, $y = \text{Height of block} + (H - h)$

$y = 105 + (105 - 70) = 140$ cm

Velocity of efflux, $v = \sqrt{2gh}$

Time of flight of water, $t = \sqrt{\dfrac{2y}{g}}$

Horizontal range, $R = v \times t = \sqrt{2gh} \times \sqrt{\dfrac{2y}{g}} = 2\sqrt{hy}$

$R = 2\sqrt{70 \times 140} = 2\sqrt{70 \times 70 \times 2} = 140\sqrt{2}$ cm

Answer: $140\sqrt{2}$