In a proof of the Pythagorean theorem using similarity what allows you to state that the triangles are similar in order to write
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408.454 cubic inches of air is surrounding the ball in the box
Step-by-step explanation:
When a sphere is inscribed in a cube and touching all of its faces, then
- The diameter of the sphere = the side of the cube
- The empty volume of the cube is the difference between the volume of the cube and the volume of the sphere
∵ The basketball is shaped a sphere
∵ The box is shaped a cube
∵ The ball touching every wall of the box
∴ The diameter of the ball = the side of the box
∵ The length of one side of the cube = 9.5 inches
∴ The diameter of the ball = 9.5 inches
∵ The diameter of the ball = 2 r, where r is the radius of the ball
∴ 9.5 = 2 r
- Divide both sides by 2
∴ r = 4.75 inches
∵ The volume of the air that surrounded the ball in the box =
volume of the box - volume of the ball
∵ Volume box (cube) = s³
∵ s = 9.5 inches
∴ Volume of the box = (9.5)³
∴ Volume of the box = 857.375 inches³
∵ Volume the ball (sphere) = π r³
∵ r = 4.75
∴ Volume the ball = (π)(4.75)³
∴ Volume the ball = 448.921 inches³
Substitute the values of the volumes of the box and the ball in the rule above
∴ The volume of the air = 857.375 - 448.921
∴ The volume of the air = 408.454 inches³
408.454 cubic inches of air is surrounding the ball in the box
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<h2>1. The "required option c) 45" is correct.</h2><h2>2. The value of 8 − 2⋅3 + 7 = 9</h2><h2>3. The required "option c) 45" is correct.</h2><h2>4. The required "option a) 40" is correct.</h2><h2>5. The value of 
= 8</h2>
Step-by-step explanation:
1. We have,
+ 20
To find, the value of + 20 = ?
∴ + 20
= 5 × 5 + 20
= 25 + 20
= 45
Thus, the "required option c) 45" is correct.
2. We have,
8 − 2⋅3 + 7
To find, the value of 8 − 2⋅3 + 7 = ?
∴ 8 − 2⋅3 + 7
= 8 - 6 + 7
= 15 - 6
= 9
Thus, the value of 8 − 2⋅3 + 7 = 9
3. We have,
To find, the value of = ?
∴
= 6 × 6 + 3 × 3
= 36 + 9
= 45
Thus, the required "option c) 45" is correct.
4. We have,
To find, the value of = ?
∴
= 2 × 2 × 2 + 4 × 8
= 8 + 32
= 40
Thus, the value of = 40
Thus, the required "option a) 40" is correct.
5 . We have,
To find, the value of = ?
∴
= 3 × 3 - 2 × 3 + 5
= 9 - 6 + 5
= 14 - 6
= 8
Thus, the value of = 8