A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.
Answers
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The volume of cone = (⅓) × π × 6 × 6 × 24 cm³
If r is the radius of the sphere, then its volume is (4/3) πr³.
Since the volume of clay in the form of the cone and the sphere remains the same,
We have:
➠ (4/3) πr³ = (⅓) × π × 6 × 6 × 24 cm³
➠ r³ = 3 × 3 × 24 = 3³ × 2³
➠ So, r = 3 × 2 = 6
- Therefore, the radius of the sphere is 6 cm.
✬ Radius of Sphere = 6 cm ✬
Step-by-step explanation:
Given:
- Height of cone is 24 cm.
- Radius of base of cone is 6 cm.
- Cone is reshaped into sphere.
To Find:
- What is the measure of radius of sphere?
Solution: As we know that Volume of cone is
★ Volume of cone = ( 1/3πr²h ) cubic units ★
1/3 π (6)² 24 cm³
1/3 π 36 24 cm³
288π cm³
If 'r' the radius of the sphere , then volume of sphere is :-
★ Volume of sphere = ( 4/3πr³ ) cubic units ★
4/3 π r³ cm³
Since, the volume of clay in the form of cone and the sphere remains the same, therefore both volumes will be equal i.e
- Volume of cone = Volume of sphere
288π = 4/3 π r³
288 = 4/3 r³
288 3 = 4 r³
864 = 4 r³
864/4 = r³
216 = r³
³√6 6 6 = r
6 cm = r
Hence, the radius of sphere is 6 cm.
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★ Other Formulae ★
➭ CSA of cone = πrl
➭ TSA of right circular cone = πr(l + r )
➭ Surface area of sphere = 4πr²