Could someone help plz
1 answer:
Answer:
The radius of the sphere is approximately 62.71 cm
Step-by-step explanation:
The question relates to the definition of a sphere
The given parameters are;
The distance between the sharp parallel blades through which the sphere is rolled = 77 centimeters
The radii of the circular faces left by cutting the sphere with the blade = 39 cm and 60 cm
From the triangles formed by the cross-section of the sphere, we have;
AB ║ DE Given
∠A ≅ ∠E, ∠D ≅ ∠B Alternate angles
∠C ≅ ∠C by reflective property
∴ ΔABC ~ ΔDCE by Angle-Angle similarity theorem
CF/CG = AB/DE = 78/120 = 13/20
CF = CG × 13/20
CF + CG = 77
∴ CG × 13/20 + CG = 77
33·CG/20 = 77
∴ CG = 140/3
CF = 13/20 × CG = 13/20 × 140/3 = 91/3
CF = 91/3
The diameter of the sphere AE = AC + EC
By Pythagoras's theorem
AC = √(FA² + CF²) = √(39² + (91/3)²) = 13·√(130)/3
EC = √(CG² + GD²) = √((140/3)² + 60²) = 20·√(130)/3
∴ AE = AC + EC = 13·√(130)/3 + 20·√(130)/3 = 11·√(130)
The diameter, 'D', of the sphere, AE = 11·√(130)
The radius of the sphere = D/2 = 11·√(130)/2 ≈ 62.71 cm
You might be interested in
Answer:
80 feet
Step-by-step explanation:
Given:
Initial speed of the car () = 40 ft/sec
Deceleration of the car () = -10 ft/sec²
Final speed of the car () = 0 ft/sec
Let the distance traveled by the car be 'x' at any time 't'. Let 'v' be the velocity at any time 't'.
Now, deceleration means rate of decrease of velocity.
So,
Negative sign means the velocity is decreasing with time.
Now, using chain rule of differentiation. Therefore,
Integrating both sides under the limit 40 to 0 for 'v' and 0 to 'x' for 'x'. This gives,
Therefore, the car travels a distance of 80 feet before stopping.