Question
- The figure shows a solid which consists of a hemisphere
and a right circular cylinder with the same base. The
height of the circular cylinder is twice its base radius. If
the volume of the solid is
, find the height of the
circular cylinder.
- In the figure, the radius of the sphere and the base radius
of the right circular cylinder are the same. The base radius
and the height of the circular cylinder are the same. If
the total volume of the two solids is
, find the
diameter of the sphere.
and a right circular cylinder with the same base. The
height of the circular cylinder is twice its base radius. If
the volume of the solid is
circular cylinder.
of the right circular cylinder are the same. The base radius
and the height of the circular cylinder are the same. If
the total volume of the two solids is
diameter of the sphere.
Ask by Warren Bob. in Hong Kong
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
問題 1
已知一個固體由一個半球和一個圓柱組成,兩者的底面半徑相同。圓柱的高度是其底面半徑的兩倍。固體的體積為
。
答案: 圓柱的高度為
。
問題 2
已知一個球體和一個圓柱的底面半徑相同,圓柱的底面半徑和高度相同。兩個固體的總體積為
。
答案: 球的直徑為
。
Solution

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Mind Expander
To solve the first problem, we recognize that the volume of the solid consists of the volume of the hemisphere and the cylinder. The volume
of a hemisphere is given by
, and the volume of a cylinder is
. Given that the height
of the cylinder is twice the base radius
, we can substitute
into the volume formula. So, the total volume becomes:
We set this equal to the given volume
:
Solving for
, we find
, which gives
, leading to
cm. The height of the cylinder is:
For the second problem, we have a sphere and a cylinder with the same radius
and the cylinder’s height
. The volume of the sphere is
, and the volume of the cylinder is
. Thus, the total volume is:
Setting this equal to
:
Dividing both sides by
and multiplying by
:
Thus,
cm. The diameter of the sphere is
cm.