Water flows at the rate of 10 m/min from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth is 24 cm?

1 hec = 10000 m³
Volume of water = Base area x Height
= (10000 x 10)/100 = 1000 m³

Given, l = Length of the cuboid = 5 x 7 = 35 cm
h = Breadth of the cuboid = 5 cm
h = Height of the cuboid = 5 cm
? Surface area = 2(lb + bh + lh) = 2[35 x 5 + 5 x 5 + 35 x 5]
= 2[175 + 25 + 175]
= 2 x 375 = 750 sq cm

Volume of the cuboid = 9 x 8 x 6 = 432 cm³
Volume of the cube = 1/2 x 432 = 216 cm³
? Each side of cube = ?216 = 6 cm
Total surface area of the cube = 6 x (Side)² = 6 x 6²
= 6 x 36 = 216 sq cm

Given, 4?r² = 2?rh
? h = 2r
Now, required ratio
= 4/3?r³ : ?r²h
= 4r : 3h
= 4r : 6r [ ? h = 2r]
= 2 : 3

Let r = Radius of cylinder = Radius of sphere, h = Height of the cylinder.
According to the question.
4/3?r³ = ?r²h
? h = 4r/3
? 4r = 3h
? 2r = 3/2h
? 2r/h = 3/2
? Required ration = 3 : 2

Let level of water will be increased by h cm
? x (15)² x h = (4/3)?(10)³
? h = [(4/3) x 10 x 10 x 10] / [15 x 15]
= 5²⁵/₂₇ cm

Volume of water = Volume of conical flask = (1/3)?r²h
Now, the water is poured into cylindrical flask.
? Volume of cylinder = Volumes of water
? ? (mr)² x Height = (1/3)?r²h
? Height = h/3m²

Given, diameter = 150 cm
? r = 150/2 cm
According to the question,
2/3? (150/2)³ = 120 ?r² x 15
? (2/3) x 150 x 150 x 150 / 8 = 120 x 15 x r²
? r² = (150 x 150 x 150) / (12 x 120 x 5)
? r² = 625/4
? r = ?625/4 = 25/2
? Diameter = 2r = 2 x 25/2 = 25 cm

Let length of the wire be h According to the question,
Volume of sphere = Volume of wire
(4/3) x ? x 18 x 18 x 18 = ? x (2/10) x (2/10) x h
? h = (100 x 1944) cm
= (100 x 1944)/100 m = 1944 m [? 1 cm = 1/100 m]

r = Radius of the cone = 14/2 = 7 cm
h = Height of the cone = 12 x 2 = 24 cm
? Slant height (l) = ?r² + h²
= ?(7)² + (24)²
= ?49 + 576
= ?625
= 25 cm
Area of the sheet = Total surface area
= (?rl + ?r²)
= ?r(l + r)
= (22/7) x 7 x (25 + 7) = 704 sq cm