Exploring Volume of Prisms and Cylinders

What type of triangle is assumed when the sides are regular?

• Isosceles

• Right

• Scalene

• Equilateral

Which theorem is used to find the slant height in the problems discussed?

• Euclidean theorem

• Pythagorean theorem

• Theorem of Pappus

• Fermat's Last Theorem

What mathematical concept is used to find the lateral area of a polygon?

• Tangent ratios

• Area of a circle

• Apothem calculation

• Circumference

How is the volume of a solid generally described?

• Amount of surface area

• Length multiplied by width

• Space inside the 3D shape

• Density times mass

What is the formula for the volume of a prism?

• Base area times height

• Base area plus height

• Length times width times height

• Base perimeter times height

According to Cavalieri's Principle, when do two shapes have the same volume?

• When they have the same height

• When they have the same surface area

• When they have the same cross-sectional area at every level

• When they are made of the same material

What does 'oblique' refer to in the context of cylinder volume calculation?

• A cylinder that is not upright

• A cylinder with a curved base

• A cylinder with varying radius

• A cylinder with a square base

How is the volume of an oblique cylinder calculated?

• Radius squared times height

• Base area times lateral height

• Pi times radius squared times vertical height

• Pi times diameter squared times height

What is the result of the volume calculation for the oblique cylinder discussed?

• 16,725.8 cubic centimeters

• 1,005.3 cubic centimeters

• 117,671.46 cubic feet

• 3,240 cubic inches

In the word problem, what is the length of each prism if the volume of prism B is 128 cubic inches greater than prism A?

• 9 inches

• 12 inches

• 8 inches

• 5 inches