A collection of dimes is arranged in a triangular array with 17 coins in the base row, 16 in the next, 15 in the next, and so fo
rth.
2 answers:
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Part a:
The opening of the cup is the circular base of the cup which has a circumference equal to the length of the arc formed by angle <span>θ = 9π/5 on the circular piece of paper from which the cone was made.
Thus, the circumference of the circle = Length of the arc formed by angle </span>θ = 9π/5 at the center which is given by
Part b:
The opening of the cup is the circular base of the cup which has a circumference equal to the length of the arc formed by angle <span>θ = 9π/5 on the circular piece of paper from which the cone was made.
</span>Recall that the circumference of a circle is given by
and having obtained from part a that the circumference of the circular opening is 
cm.
Thus,
Part c:
The height of the cup can be obtained by noticing that the radius, height and the slant height of the cup forms a right triangle with the height and the radius as the legs and the slant height as the hypothenus.
Using pythagoras theorem, the height of the cup is obtained as follows:
where: h is the height, r is the radius and l is the slant height.
Part d
Recall that the volume of a cone is given by
Thus, the volume of the cup is given by
The opening of the cup is the circular base of the cup which has a circumference equal to the length of the arc formed by angle <span>θ = 9π/5 on the circular piece of paper from which the cone was made.
Thus, the circumference of the circle = Length of the arc formed by angle </span>θ = 9π/5 at the center which is given by
Part b:
The opening of the cup is the circular base of the cup which has a circumference equal to the length of the arc formed by angle <span>θ = 9π/5 on the circular piece of paper from which the cone was made.
</span>Recall that the circumference of a circle is given by
Thus,
Part c:
The height of the cup can be obtained by noticing that the radius, height and the slant height of the cup forms a right triangle with the height and the radius as the legs and the slant height as the hypothenus.
Using pythagoras theorem, the height of the cup is obtained as follows:
where: h is the height, r is the radius and l is the slant height.
Part d
Recall that the volume of a cone is given by
Thus, the volume of the cup is given by