Question

!50 POINTS! (2 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW

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Answer 1

For 1st Question: (c).Rhombus

For 2nd Question: 27 times

The volume of the cone is multiplied by 27 times.

Explanation:

For the 1st Question:

• A parallelogram has opposite sides that are parallel and congruent, but the diagonals of a parallelogram are not necessarily perpendicular bisectors of each other.
• A rectangle is a special type of parallelogram that has all four right angles. This means that the diagonals of a rectangle are perpendicular, but they are not necessarily perpendicular bisectors of each other.
• A rhombus is a quadrilateral with all four sides of equal length. This means that the opposite sides of a rhombus are parallel and congruent, and the diagonals of a rhombus are perpendicular bisectors of each other.
• A trapezoid is a quadrilateral with one set of parallel sides. The diagonals of a trapezoid are not necessarily perpendicular bisectors of each other.

Therefore, the only shape that must have opposite sides that are parallel and congruent, and diagonals that are perpendicular bisectors of each other is a rhombus. So the answer is (c).Rhombus

`\hrulefill`

For 2nd Question:

The volume of a cone is given by the formula:

`\boxed{\sf Volume = (1)/(3) * \pi * r^2 * h}`

where r is the radius and h is the height of the cone.

If the radius and height are each multiplied by 3, then the new volume is:

`\sf New\: Volume = (1)/(3)* \pi * (3r)^2 * (3h) = 27 *\left((1)/(3)* \pi* r^2 * h\right)`

Therefore,

The volume of the cone is multiplied by 27 times.