Question

1. find the surface area of the cone to the nearest mm².
2. find the surface area of the cylinder to the nearest m².
3. find the surface area of the square pyramid to the nearest ft².

Explanation:

12. Cone

Step1: Recall surface - area formula

The surface - area formula of a cone is $A=\pi r(r + l)$, where $r$ is the radius and $l$ is the slant height. Given $r = 4$ mm and $l=6$ mm.

Step2: Substitute values

$A=\pi\times4\times(4 + 6)$.
$A = 40\pi$ mm².

Step3: Calculate the value

$A\approx40\times3.14159=125.6636$ mm². Rounding to the nearest mm², $A\approx126$ mm².

Step1: Recall surface - area formula

The surface - area formula of a cylinder is $A = 2\pi r(r+h)$, where $r$ is the radius and $h$ is the height. Given $r=\frac{8}{2}=4$ cm and $h = 16$ cm.

Step2: Substitute values

$A=2\pi\times4\times(4 + 16)$.
$A=2\pi\times4\times20=160\pi$ cm².
Since we want the answer in m², convert cm² to m². $1$ m²=$10000$ cm², so $A=\frac{160\pi}{10000}$ m².

Step3: Calculate the value

$A=\frac{160\times3.14159}{10000}=0.05026544$ m². Rounding to the nearest m², $A\approx0$ m².

Step1: Recall surface - area formula

The surface - area formula of a square pyramid is $A = s^{2}+2sl$, where $s$ is the base side length and $l$ is the slant height. Given $s = 5$ ft and $l = 10$ ft.

Step2: Substitute values

$A=5^{2}+2\times5\times10$.
$A = 25+100$.

Step3: Calculate the value

$A=125$ ft².

Answer:

$126$ mm²

13. Cylinder