Math question need help!

Mathematics

1 answer:

Blababa [14]4 years ago

7 0

The volume of the remaining solid can be calculated by subtracting the volume of the cylindrical hole from the volume of the original box.

1- getting volume of original box:
We have:
length of box = 24 cm
width of box = 16 cm
height of box = 16 cm
Since the box has a rectangular shape, therefore:
volume of box = length * width * height
volume of box = 24 * 16 * 16 = 6144 cm^3

2- getting the volume of cylindrical hole:
We have:
radius of hole = 4 cm
height of hole = 24 cm (as it goes along the hole length of the original box)
Volume pf cylinder = pi * r^2 * h
volume of cylinder = pi * (4)^2 * 24 = 1206.371579 cm^3

3- getting volume of remaining solid:
volume of remaining solid = volume of box - volume of cylinder
volume of remaining solid = 6144 - 1206.371579 = 4937.628421 cm^3

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Answer:

Step-by-step explanation:

The angles given are 62° and 90°.

We know sum of angles in any triangle is 180° so the third angle must be 180-90-62 = 28°

We can find the sides if we know trigonometric functions

sin28° = opp. side/ hypothenuse = CA/BA = 8/BA

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tan62°= opp.side/adj.side= BC/AC = BC/8

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We are given 2 sides 8.5 and 6.5 and that one angle is right, so the triangle is a right triangle, therefore we can apply Pythagorean Theorem to find the third side.

6.5² +FD² = 8.5², subtract 6.5² from both sides

FD² = 8.5²- 6.5², square and combine like terms

FD² = 30, square-root both sides

FD = √30

FD ≈ 5.47722, round to the nearest tenth

FD ≈ 5.5

We can find the angles if we know trigonometric functions.

sin ∡D = FE/DE = 6.5/8.5

∡D = sin^-1 (6.5/8.5)

∡D ≈ 49.9°

cos ∡E = FE/DE = 6.5/8.5

∡E = cos^-1 (6.5/8.5)