Find the volume of a cone with base area 36π ft2 and a height equal to twice the radius. Give your answers both in terms of π and rounded to the nearest tenth.
The volume in terms of π is ft3.
The volume rounded to the nearest tenth is ft3.

The volume in terms of π is 144 ft³

The volume rounded to the nearest tenth is 452.4 ft³

Step-by-step explanation:

The formula of the volume of a cone is V = π r² h , where r is its radius and h is its height

The formula of the area of a circle is A = π r²

∵ The area of the base of the cone is 36π ft²

- Equate the formula of the area of the circle by 36π to find r

∵ πr² = 36π

- Divide both sides by π

∴ r² = 36

- Take √ to both sides

∴ r = 6 ft

∵ The height of the cone is equal to twice the radius

∵ The radius of the cone is 6 ft

- Multiply 6 by 2 to find the height

∴ h = 2(6) = 12 ft

∴ The height of the cone is 12 ft

Substitute the values of h and r in the formula of the volume of the cone to find it

∵ V = π(6)²(12)

∴ V = 144 π ft³

∴ V = 452.3893421 ft³

- Round it to the nearest tenth

∴ V = 452.4 ft³

b

step-by-step explanation:

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)