Learning Task 1:Find the volume of the second picture using the volume of the first given. The given solid figures have the same base and height.
1. The volume of the cylinder is 78 cubic cm,find the volume of the cone.
2.The volume of the pyramid is 36 cubic cm,find the volume of the prism.
3.The volume of the cylinder is 198m³, find the volume of the given sphere.
4.The volume of the sphere is 68.5m³,find the volume of the cylinder with the same base and height. The volume of the pyramid is 45.5m³,find the volume of a prism with same base and height.
Answers
Answer: Yes
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Step-by-step explanation: Yes
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Answer:
1. If a cone and cylinder have the same base and height. The volume of a cylinder is three times that of a cone.
The formula for a cone's volume; V= 1/3πr^2*h
The volume formula for a cylinder;V=πr^2 *h
Because they have the same height and base. As a result, the cone's volume is;
V=1/3*78=26 cm^3
2. Given : volume of the pyramid is 36 cubic cm,
To determine the prism volume
Solution:
Assume that the area of the base of the pyramid and the height of the prism are both A and H.
Prism volume = base area * height
Prism Volume = AH
Pyramid volume = (1/3)height * base area
Volume of Pyramid = (1/3) AH
Volume of Pyramid = 36 cubic cm
V= (1/3) AH = 36
= AH = 36 * 3
=AH = 108
So the Volume of Prism 108 cm^{3}
3. Given; The volume of the cylinder is 198 m^{3}
The volume of the provided sphere must be determined.
Solution;
Volume of sphere=4/3πr^3
Volume of cylinder= πr^2h
On dividing
Volume of sphere/Volume of cylinder=(4/3πr^3)/(2πr^3)
Volume of sphere/198=4/6
Volume of sphere=132m^3
So the volume of sphere is 132 m^{3}
4. Suppose the radius of the sphere is R,
Volume of sphere;
4/3πr^3=67.5m^3
πr^3=50.625 m^{3}
Volume of cylinder =πr^2*2r
= 2πr^3
=101.25m^{3}
5. Assuming the area of base of pyramid is "s" and the height is "h".
Volume of the pyramid= 1/3sh
Volume of prism= sh
Hence;
Volume of prism=3Volume of pyramid (Substitution)
=45.5m^3X3
=45.5m^3X3 =136.5m^{3}