The the radius , the centimeters of the greatest sphere that can be carved out of a solid cone of radius 9 cm and height 40 cm is
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Radius of Greatest sphere = 7.20 meter
Step-by-step explanation:
The greatest sphere that can be carved out of a solid cone of radius 9 cm and height 40 cm is :
Slant height of sphere = l²= h²+ r²
l² = 40² +9²
l² = 1681
l = 41 meter
Let the greatest sphere has radius R.
As sphere will touch the base as well as other two sides of the cone.
Line segment PS will be tangent to the sphere at point M.
So, ∠PMO= 90°
As, PR ⊥ QS, ∠PRS = 90°
In Δ PRS, and Δ PMO
m∠PRS = m∠PMO = 90°
∠MPR = ∠SPR [Common Angles]
By AA postulate of Similarity of triangles. We get, ΔPRS ~ ΔPMO
Hence, Radius of Greatest sphere = 7.20 meter.
Step-by-step explanation:
The greatest sphere that can be carved out of a solid cone of radius 9 cm and height 40 cm is :
Slant height of sphere = l²= h²+ r²
l² = 40² +9²
l² = 1681
l = 41 meter
Let the greatest sphere has radius R.
As sphere will touch the base as well as other two sides of the cone.
Line segment PS will be tangent to the sphere at point M.
So, ∠PMO= 90°
As, PR ⊥ QS, ∠PRS = 90°
In Δ PRS, and Δ PMO
m∠PRS = m∠PMO = 90°
∠MPR = ∠SPR [Common Angles]
By AA postulate of Similarity of triangles. We get, ΔPRS ~ ΔPMO
Hence, Radius of Greatest sphere = 7.20 meter.
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