volume and surface area Cones

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 = πr(r + l), where r is the radius of the base and l is the slant height.

Front

What is the formula for the volume of a cone?

Back

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

Front

If a cone has a radius of 3 cm and a height of 4 cm, what is its volume?

Back

V = (1/3)π(3^2)(4) = 12π cm³ ≈ 37.70 cm³.

Front

What is the slant height of a cone with a radius of 5 cm and a height of 12 cm?

Back

The slant height (l) can be found using the Pythagorean theorem: l = √(r^2 + h^2) = √(5^2 + 12^2) = √(25 + 144) = √169 = 13 cm.

Front

How do you calculate the lateral surface area of a cone?

Back

The lateral surface area (LSA) of a cone is calculated using the formula: LSA = πrl, where r is the radius and l is the slant height.

Front

What is the relationship between the radius, height, and slant height of a cone?

Back

The relationship is given by the Pythagorean theorem: l = √(r^2 + h^2), where l is the slant height, r is the radius, and h is the height.

Front

Find the surface area of a cone with a radius of 4 cm and a slant height of 5 cm.

Back

SA = πr(r + l) = π(4)(4 + 5) = π(4)(9) = 36π cm² ≈ 113.10 cm².

Front

What is the total surface area of a cone?

Back

The total surface area of a cone includes the base area and the lateral area: Total SA = πr^2 + πrl.

Front

If a cone has a diameter of 10 cm, what is its radius?

Back

The radius (r) is half of the diameter: r = diameter/2 = 10 cm / 2 = 5 cm.

Front

What is the surface area of a cone with a height of 6 cm and a radius of 3 cm?

Back

First, find the slant height: l = √(3^2 + 6^2) = √(9 + 36) = √45 = 6.71 cm. Then, SA = π(3)(3 + 6.71) = π(3)(9.71) ≈ 91.24 cm².