3. square pyramid: volume $$ 1,024 \mathrm{~cm}^{3} $$; base edae 16 cm

Question

UpStudy AI · Accepted Answer

Let the volume $$ V $$ of a square pyramid be given by

$$
V = \frac{1}{3} B h,
$$

where $$ B $$ is the area of the base and $$ h $$ is the height.

1. **Calculate the base area:**

Since the base is a square with edge length $$ 16 $$ cm, the area is

$$
   B = 16^2 = 256 \, \mathrm{cm}^2.
   $$

2. **Substitute the known values into the volume formula:**

$$
   1024 = \frac{1}{3} \times 256 \times h.
   $$

3. **Solve for $$ h $$:**

Multiply both sides by 3 to isolate $$ h $$ on one side:

$$
   1024 \times 3 = 256h.
   $$

$$
   3072 = 256h.
   $$

Now, divide both sides by 256:

$$
   h = \frac{3072}{256} = 12 \, \mathrm{cm}.
   $$

The height of the square pyramid is $$ 12 \, \mathrm{cm} $$.
The height of the square pyramid is 12 cm.

3. square pyramid: volume \( 1,024 \mathrm{~cm}^{3} \); base edae 16 cm