Surface area of pyramids and cones

Front

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

Back

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

Front

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

Back

The area of the base (B) of a square pyramid is calculated using the formula: B = s^2, where s is the length of one side of the square base.

Front

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

Back

The slant height (l) of a pyramid is the distance from the apex to the midpoint of a side of the base. It can be found using the Pythagorean theorem: l = rac{1}{2}b^2 + h^2, where b is the base length and h is the height.

Front

What is the perimeter of the base of a cone with radius r?

Back

The perimeter (P) of the base of a cone is calculated using the formula: P = 2 ext{π}r, where r is the radius of the base.

Front

How do you find the surface area of a cone with a radius of 3 cm and a slant height of 5 cm?

Back

Using the formula SA = rac{1}{2}Pl + B, first calculate P = 2 ext{π}(3) = 6 ext{π} cm. Then, B = ext{π}(3^2) = 9 ext{π} cm². Finally, SA = rac{1}{2}(6 ext{π})(5) + 9 ext{π} = 15 ext{π} + 9 ext{π} = 24 ext{π} cm².

Front

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

Back

First, find the slant height using the Pythagorean theorem: l = ext{√}(r^2 + h^2) = ext{√}(4^2 + 3^2) = 5 cm. Then, use the surface area formula: SA = rac{1}{2}(2 ext{π}(4))(5) + ext{π}(4^2) = 40 ext{π} cm².

Front

What is the surface area of a square pyramid with a base side of 6 cm and a slant height of 8 cm?

Back

Calculate the base area: B = 6^2 = 36 cm². Then, find the perimeter: P = 4(6) = 24 cm. Finally, use the formula: SA = B + rac{1}{2}Pl = 36 + rac{1}{2}(24)(8) = 36 + 96 = 132 cm².

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

How do you round a surface area to the nearest hundredth?

Back

To round a number to the nearest hundredth, look at the third decimal place. If it is 5 or greater, round up the second decimal place by one. If it is less than 5, keep the second decimal place the same.