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 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 = \frac{1}{3}πr^2h, where r is the radius and h is the height.

Front

If a cone has a radius of 5 ft and a slant height of 13 ft, what is its surface area?

Back

The surface area is approximately 282.74 ft².

Front

What is the height of a cone if the radius is 6 in and the volume is 150 in³?

Back

To find the height, use the volume formula: V = \frac{1}{3}πr^2h. Rearranging gives h = \frac{3V}{πr^2}. Plugging in the values gives h = 25 in.

Front

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

Back

The slant height (l) can be found using the Pythagorean theorem: l = \sqrt{r^2 + h^2} = \sqrt{5^2 + 12^2} = 13 ft.

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 = \sqrt{r^2 + h^2}, where l is the slant height, r is the radius, and h is the height.

Front

Find the volume of a cone with a height of 4 in and a radius of 6 in.

Back

The volume is 150 in³.

Front

What is the surface area of a cone with a radius of 10 cm and a slant height of 15 cm?

Back

The surface area is approximately 392.70 cm².

Front

What is the formula to find the radius of a cone if the volume and height are known?

Back

Rearranging the volume formula gives r = \sqrt{\frac{3V}{πh}}.