8.MG.2.d

Front

What is the formula for the surface area of a square-based pyramid?

Back

The surface area (SA) of a square-based pyramid is given by the formula: SA = base area + lateral area = b^2 + 2 * b * l, where b is the base side length and l is the slant height.

Front

What is the volume formula for a cone?

Back

The volume (V) of a cone is given by the formula: V = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height.

Front

How do you determine if a problem is asking for surface area or volume?

Back

Surface area measures the total area of the surface of a 3D shape, while volume measures the amount of space inside the shape. Look for keywords: 'area' indicates surface area, while 'capacity' or 'how much' indicates volume.

Front

What is the slant height of a pyramid?

Back

The slant height is the distance from the apex (top point) of the pyramid to the midpoint of one of the edges of the base.

Front

Calculate the surface area of a square-based pyramid with a base side length of 5 cm and a slant height of 8 cm.

Back

SA = 5^2 + 2 * 5 * 8 = 25 + 80 = 105 cm².

Front

What is the relationship between the radius and height in a cone?

Back

The radius is the distance from the center of the base to the edge, while the height is the perpendicular distance from the base to the apex. Both are used in the volume formula.

Front

If a cone has a radius of 5 m and a height of 12 m, what is its volume?

Back

V = (1/3) * π * (5^2) * 12 = (1/3) * 3.14 * 25 * 12 = 314 m³.

Front

What does the term 'base area' refer to in the context of pyramids?

Back

Base area refers to the area of the base shape of the pyramid. For a square base, it is calculated as b^2, where b is the length of one side.

Front

What is the significance of the slant height in calculating the surface area of a pyramid?

Back

The slant height is crucial for calculating the lateral area of the pyramid, which contributes to the total surface area.

Front

What is the formula for the surface area of a cone?

Back

The surface area (SA) of a cone is given by the formula: SA = π * r * (r + l), where r is the radius and l is the slant height.