Question

A solid metal cylinder of base radius 15cms and height 32cms is melted down and recast
into a cylinder of base radius 20cms. What is the height of this cylinder?
2. A water tank in the shape of a prism has isosceles trapezium as bases whose dimensions
are shown belew​

Answer 1

Answer:

$Radius_1(r_1) = 15cm\\height_1(h_1) \ = 32cm\\Radius_2(r_2) = 20cm\\height_2(h_2) \ = h_2\\\\Volume_1 = Volume_2\\\\\pi (r_1)^{2}h_1 = \pi (r_2)^{2}h_2\\\\\pi (15)^{2}(32) = \pi (20)^{2}(h_2)\\\\\pi (225) \times (32) = \pi (400) \times (h_2)\\\\h_2 =\frac{\pi \times 225 \times 32}{\pi \times 400} \\\\ h_2 = \frac{225 \times 32}{400}\\\\\therefore h_2 = \frac{(25) \times 9 \times (4) \times (4) \times 2}{(4) \times (25) \times (4)}\\\\\therefore h_2 = 9 \times 2\\\therefore h_2 = 18cm$

Step-by-step explanation: