Volume problems? 10 POINTS

PLEASE ANSWER!

pg 730 #12~14 and #17~19

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12.) You have the side length of the base and the slant height. To find the height, solve using the Pythagorean Theorem. Make "a" half of the base (5) and "c" the slant height (12).
5^2 + b^2 = 12^2
25 + b^2 = 144
b^2 = 119
b = √119

Now that you know the area of the base and the height, you can solve for the volume:
V = Bh/3
V = (10^2)(√119)/3
V = 100(√119) / 3
V ≈ 363.6 m^3


13.) You have the side length of the base and the slant height. To find the height, solve using the Pythagorean Theorem. Make "a" half of the base (11.5) and "c" the slant height (24).
(11.5)^2 + b^2 = 24^2
132.25 + b^2 = 576
b^2 = 443.75
b = √(443.75)

Now that you know the area of the base and the height, you can solve for the volume:
V = Bh/3
V = (23^2)(√443.75) / 3
V = 529(√443.75) / 3
V ≈ 3714.5 mm^3


14.) You have the side length of the base and the slant height. To find the height, solve using the Pythagorean Theorem. Make "a" half of the base (5.5) and "c" the slant height (15).
(5.5)^2 + b^2 = 15^2
30.25 + b^2 = 225
b^2 = 194.75
b = √194.75

Now that you know the area of the base and the height, you can solve for the volume:
V = Bh/3
V = (11^2)(√194.75) / 3
V = 121(√194.75) / 3
V ≈ 562.9 ft^3


17.) You have the diameter and the height. To find the radius, divide the diameter by 2, which gives you a radius of 2. The area of the base is:
A = πr^2
A = π(2^2)
A = 4π

Now that you know the area of the base and the height, you can solve for the volume:
V = Bh/3
V = 4(4π) / 3
V = 16π/3
V ≈ 17 ft^3


18.) You have the diameter and the height. To find the radius, divide the diameter by 2, which gives you a radius of 2. The area of the base is: