Surface Area of Pyramids and Cones

Front

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

Back

The surface area of a pyramid is given by the formula: \( SA = B + \frac{1}{2} P l \) where \( B \) is the area of the base, \( P \) is the perimeter of the base, and \( l \) is the slant height.

Front

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

Back

The surface area of a cone is given by the formula: \( SA = \pi r^2 + \pi r l \) where \( r \) is the radius of the base and \( l \) is the slant height.

Front

How do you find the slant height of a cone?

Back

The slant height \( l \) of a cone can be found using the Pythagorean theorem: \( l = \sqrt{r^2 + h^2} \) where \( r \) is the radius and \( h \) is the height of the cone.

Front

What is the difference between lateral surface area and total surface area?

Back

Lateral surface area refers to the area of the sides of a 3D shape, excluding the base(s). Total surface area includes the lateral surface area plus the area of the base(s).

Front

What is the area of a circle?

Back

The area of a circle is given by the formula: \( A = \pi r^2 \) where \( r \) is the radius of the circle.

Front

If the radius of a cone is doubled, how does the surface area change?

Back

If the radius \( r \) of a cone is doubled, the surface area increases by a factor of four, since the area is proportional to the square of the radius.

Front

What is the perimeter of a base of a pyramid?

Back

The perimeter of the base of a pyramid is the total length of all the sides of the base shape. For a square base, it is \( P = 4s \) where \( s \) is the length of a side.

Front

How do you calculate the surface area of a square pyramid?

Back

The surface area of a square pyramid is calculated using the formula: \( SA = s^2 + 2s l \) where \( s \) is the length of a side of the base and \( l \) is the slant height.

Front

What is the relationship between the height and slant height of a pyramid?

Back

The height and slant height of a pyramid are related through the Pythagorean theorem. If \( h \) is the height and \( l \) is the slant height, then \( l = \sqrt{h^2 + \left(\frac{s}{2}\right)^2} \) for a square base.

Front

What is the surface area of a cone with a radius of 3 cm and a height of 4 cm?

Back

First, find the slant height: \( l = \sqrt{3^2 + 4^2} = 5 \) cm. Then, use the surface area formula: \( SA = \pi(3^2) + \pi(3)(5) = 9\pi + 15\pi = 24\pi \approx 75.4 \text{ cm}^2 \).