Question

test 35
answer with proper units. if an answer is irrational, give both an exact (unrounded) statement of this
answer and a second answer rounded to two decimal places. show all answers on this side of this page,
as indicated.

1. find the volume of a square pyramid given ( a = 60 ) mm, ( h = 11 ) mm.

answer:

1. find the surface area of a cylinder given ( h = 1 ) mm, ( r = 24 ) mm.

answer:

1. find the surface area of a rectangular prism given ( h = 10 ) cm, ( l = 13 ) cm, ( w = 9 ) cm.

answer:

Explanation:

Step1: Volume of square pyramid formula

The formula for the volume $V$ of a square pyramid is $V = \frac{1}{3}a^2h$, where $a$ is the base edge length and $h$ is the height.

Step2: Substitute given values

Substitute $a = 60\ \text{mm}$, $h = 11\ \text{mm}$:
$V = \frac{1}{3} \times (60)^2 \times 11$

Step3: Calculate the volume

First compute $60^2 = 3600$, then:
$V = \frac{1}{3} \times 3600 \times 11 = 1200 \times 11 = 13200$

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Step1: Surface area of cylinder formula

The total surface area $S$ of a cylinder is $S = 2\pi r^2 + 2\pi rh$, where $r$ is the radius and $h$ is the height.

Step2: Substitute given values

Substitute $r = 24\ \text{mm}$, $h = 1\ \text{mm}$:
$S = 2\pi (24)^2 + 2\pi (24)(1)$

Step3: Compute each term

First term: $2\pi \times 576 = 1152\pi$; Second term: $2\pi \times 24 = 48\pi$

Step4: Sum the terms

$S = 1152\pi + 48\pi = 1200\pi$

Step5: Calculate decimal approximation

$1200\pi \approx 1200 \times 3.1416 = 3769.92$

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Step1: Surface area of rectangular prism formula

The surface area $S$ of a rectangular prism is $S = 2(lw + lh + wh)$, where $l$ is length, $w$ is width, $h$ is height.

Step2: Substitute given values

Substitute $l = 13\ \text{cm}$, $w = 9\ \text{cm}$, $h = 10\ \text{cm}$:
$S = 2[(13 \times 9) + (13 \times 10) + (9 \times 10)]$

Step3: Calculate each product

$13 \times 9 = 117$, $13 \times 10 = 130$, $9 \times 10 = 90$

Step4: Sum the products

$117 + 130 + 90 = 337$

Step5: Compute final surface area

$S = 2 \times 337 = 674$

Answer:

1. $13200\ \text{mm}^3$
2. Exact: $1200\pi\ \text{mm}^2$, Rounded: $3769.92\ \text{mm}^2$
3. $674\ \text{cm}^2$