Surface Area and Volume Concepts

The video tutorial from G Dartmouth Academy covers the calculation of surface area for combined objects, including cones, cylinders, hemispheres, prisms, and complex shapes. It explains common mistakes students make, such as incorrectly including circular areas in total surface area calculations. The tutorial provides step-by-step methods to find the surface area of each shape, emphasizing the importance of focusing on curved surfaces. It also covers the surface area of a prism by dividing it into rectangular parts and calculating each separately. Finally, it addresses the surface area of a combination of triangles and rectangles.

What are the three objects combined in the first example discussed in the video?

• Cone, Cylinder, Hemisphere

• Sphere, Cube, Cone

• Cylinder, Cube, Sphere

• Cone, Sphere, Cube

What is a common mistake students make when calculating the total surface area of combined objects?

• Including only the curved surfaces

• Ignoring the base areas

• Calculating only the volume

• Adding all individual surface areas without considering overlaps

Which formula is used to calculate the curved surface area of a cone?

• πrl

• πr²

• 2πr²

• 2πrh

What is the slant height of the cone if the vertical height is 12 cm and the radius is 5 cm?

• 10 cm

• 13 cm

• 15 cm

• 17 cm

How is the curved surface area of a hemisphere calculated?

• 2πr²

• 4πr²

• πr²

• 3πr²

What is the total surface area of the first composite object discussed?

• 700 cm²

• 675 cm²

• 650 cm²

• 625 cm²

What is the first step in calculating the surface area of a prism?

• Calculating the perimeter

• Finding the volume

• Dividing the shape into rectangular parts

• Measuring the height

How many rectangular parts are labeled in the prism example?

• 5

• 8

• 6

• 7

What is the total surface area of the prism discussed in the video?

• 336 cm²

• 350 cm²

• 320 cm²

• 340 cm²

In the U-shape composite object, what is the area of the front U-shape?

• 50 cm²

• 60 cm²

• 56 cm²

• 54 cm²