A hemispherical tank is filled with water and has a diameter of 4 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?

The total weight of the water in a full tank, to the nearest pound is 1056 pounds, if water filled with water in the 4 diameter hemispherical tank and weighs 62.4 pounds per cubic foot.

Step-by-step explanation:

         The given is,

              A hemispherical tank is filled with water and has a diameter of 4 feet.

              Water weighs 62.4 pounds per cubic foot

Step:1

             Formula to weight of water is,

                          = Volume of water tank × weight of water per foot......(1)

Step:2

             Formula to find volume of the tank is,

                        ...................................(2)

             From given, r = Radius of Hemisphere

                         r = 2 foot    

            From equation (2),        

                            = × ×

                            = 16.755 cubic foot

Step:3

            From equation (1),

                            = 16.775 × 62.4              (∵ Water weighs 62.4 pounds per cubic foot )

                            = 1045.52 pounds        ( ∵ × = )

                            ≅ 1046 pounds

            Weight of water in tank = 1046 pounds

Result:

           The total weight of the water in a full tank, to the nearest pound is 1056 pounds, if a hemispherical tank is filled with water and it has 4 feet diameter and water weighs 62.4 pounds per cubic foot.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.