Question 6 1 pts A square pyramid has a volume of 484cm^(3) and a height of 12cm. Find the length. 11cm 40.3cm 121cm

Identify Formula: Identify the formula for the volume of a square pyramid. Volume = (1/3) * base area * height Here, the base area is the area of the square base, which can be calculated as side length squared (s^2). So, Volume = (1/3) * s^2 * height Given: Volume = 484 cm^3, height = 12 cm We need to find the side length (s).Substitute and Solve: Substitute the given values into the volume formula and solve for s^2. 484 cm^3 = (1/3) * s^2 * 12 cm To isolate s^2, multiply both sides by 3 and divide by 12. (3 * 484 cm^3) / 12 = s^2Calculate s^2: Calculate the value of s^2. s^2 = (3 * 484 cm^3) / 12 s^2 = 1452 cm^3 / 12 s^2 = 121 cm^2Find Side Length: Find the side length (s) by taking the square root of s^2. s = √121 cm^2 s = 11 cm

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Question 6
1 pts
A square pyramid has a volume of
484cm^(3) and a height of
12cm. Find the length.

11cm

40.3cm

121cm

Question $6$ $\newline$ $1$ pts $\newline$ A square pyramid has a volume of $484 \mathrm{~cm}^{3}$ and a height of $12 \mathrm{~cm}$ . Find the length. $\newline$ $11 \mathrm{~cm}$ $\newline$ $40.3 \mathrm{~cm}$ $\newline$ $121 \mathrm{~cm}$

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Math Problems

Grade 6

Volume of cubes and rectangular prisms: word problems

Full solution

Q. Question

6

\newline

1

pts

\newline

A square pyramid has a volume of

484 \mathrm{~cm}^{3}

and a height of

12 \mathrm{~cm}

. Find the length.

\newline

11 \mathrm{~cm}

\newline

40.3 \mathrm{~cm}

\newline

121 \mathrm{~cm}

Identify Formula: Identify the formula for the volume of a square pyramid. $\newline$ Volume = $(\frac{1}{3}) \times \text{base area} \times \text{height}$ $\newline$ Here, the base area is the area of the square base, which can be calculated as side length squared $(s^2)$ . $\newline$ So, Volume = $(\frac{1}{3}) \times s^2 \times \text{height}$ $\newline$ Given: Volume = $484 \, \text{cm}^3$ , height = $12 \, \text{cm}$ $\newline$ We need to find the side length $(s)$ .
Substitute and Solve: Substitute the given values into the volume formula and solve for $s^2$ . $\newline$ $484 \, \text{cm}^3 = \left(\frac{1}{3}\right) \cdot s^2 \cdot 12 \, \text{cm}$ $\newline$ To isolate $s^2$ , multiply both sides by $3$ and divide by $12$ . $\newline$ $\left(3 \cdot 484 \, \text{cm}^3\right) / 12 = s^2$
Calculate $s^2$ : Calculate the value of $s^2$ .
$s^2 = \frac{3 \times 484 \text{ cm}^3}{12}$
$s^2 = \frac{1452 \text{ cm}^3}{12}$
$s^2 = 121 \text{ cm}^2$
Find Side Length: Find the side length $s$ by taking the square root of $s^2$ . $s = \sqrt{121} \, \text{cm}^2$ $s = 11 \, \text{cm}$