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100
What is a chord?
line segment whose endpoints are on surface of sphere
100
What is a secant?
A line intersects sphere at more than 1 point
100
What is the formula for the surface area of a sphere?
Surface area of the sphere = 4πr², where “r” is the sphere's radius
200
A plane is 20 m away from a sphere. If the radius of the sphere is 3 m, how far is the farthest point of the sphere from the plane?
d=r*2=3*2=6
6+20=26 m
Answer: 26 m
200
If the distance between the centers of two externally tangent spheres is 13 cm and the radius of the smaller sphere is 5 cm, find the diameter of the other sphere.
r + 5 = 13
r = 8
d = 2r = 8*2 = 16 cm
200
What is tangent?
A line that touches the circle at a single point is known as a tangent to a circle
300
A spherical segment of two bases and a frustum of a cone have the same bases and the same altitude. Which solid has the biggest volume?
V_seg = (1/6)πh(3r₁² + 3r₂² + h²)
V_frustum = (1/3)πh(R₁² + R₂² + R₁R₂)
Answer: spherical segment of two bases - it has an extra term h²
300
What is spherical sector?
If a sector of a semicircle is rotated around the diameter of the semicircle, the generated portion is called a spherical sector
300
In a sphere of 10 cm radius, a plane 8 cm away from the center forms a segment of a base. What is area of the base?
Since the points O, C, and B form a right triangle, we have r^2 = OC2 + r1^2
r1^2 = 10^2 - 8^2 = 36
A = πr1^2, the area of the circle with the center C is A = 36 πcm^2
the area of the circle with the center C is A = 36 πcm^2
400
A wedge is removed from a sphere with radius 25 cm. Find the total length of the edges of the wedge.
l² = r² + h² l² = (25)² + (25)²
l² = 625 + 625
l² = 1250
l = √1250 = 25√2
Total length of edges = C + 2l = 50π + 2*25√2 = 50(π + 1) cm
400
How many wedges of 72° angle can we cut a sphere into?
Since one whole sphere is 360°, we can cut a sphere into 360°/72° = 5 wedges of 72°
400
A spherical segment of two bases in a sphere has a height of 24 cm. The radius of the sphere is 20 cm. One base area of the segment is 256r cm? What is the area of its other base?
R₂ = 2r - R₁
R₂ = 2(20) - 24 = 16 cm
A₂ = πR₂² = π(16)² = 256π cm²