Geometry Concepts and Problem Solving

This video tutorial covers Unit 12, focusing on the volume of solids. It begins with a review of area calculations for squares, circles, and triangles, then moves on to volume calculations for prisms, cylinders, composite solids, cones, pyramids, and spheres. The tutorial also includes comparisons of volumes between different shapes and practical problem-solving exercises.

What is the area of a square with a side length of 17 cm?

• 289 cm²

• 34 cm²

• 68 cm²

• 17 cm²

How do you calculate the area of a circle with a diameter of 17 cm?

• π × 8.5²

• π × 17²

• π × 4.25²

• π × 34²

What is the area of a triangle with a base of 8 cm and a height of 4 cm?

• 8 cm²

• 4 cm²

• 32 cm²

• 16 cm²

In a 30-60-90 triangle, if the hypotenuse is 30, what is the length of the side opposite the 30-degree angle?

• 30√3

• 15√3

• 30

• 15

If the circumference of a circle is 8π, what is the radius?

• 2

• 8

• 16

• 4

How do you calculate the volume of a triangular prism?

• Base area × height

• Length × width × height

• π × radius² × height

• 1/3 × base area × height

What is the volume of a cylinder with a radius of 7 cm and a height of 12 cm?

• 588π cm³

• 49π cm³

• 84π cm³

• 168π cm³

How do you find the volume of a composite shape like a prism with a hole?

• Multiply the volumes of all parts

• Add the volumes of all parts

• Divide the volume of the outer shape by the volume of the hole

• Subtract the volume of the hole from the volume of the outer shape

What is the formula for the volume of a cone?

• 1/2 × base area × height

• Base area × height

• 1/3 × π × radius² × height

• π × radius² × height

How do you find the height of a pyramid if given the slant height and base edge?

• Use the Pythagorean theorem

• Multiply the slant height by the base edge

• Divide the slant height by the base edge

• Add the slant height and base edge