A small square pyramid of height 6 cm was removed from the top of a large square pyramid of height 12cm forming the solid shown.

Question

3 years ago

12

Find the exact volume of the solid

2 answers:

charle [14.2K] · Answer 1 · 2022-02-04T12:24:40+03:00

Answer:

15,872 mm³

Step-by-step explanation:

bottom volume = total volume - the volume on top

total volume = 1/3 (base area)² h

= 1/3 (8*8)² * 12

= 16,384 mm³

volume on top = 1/3 (top base area)² h

= 1/3 (4*4)² * 6

= 512 mm³

bot. vol = 16,384 mm³ - 512 mm³ = 15,872 mm³

Semmy [17] · Answer 2 · 2022-02-04T11:00:21+03:00

Answer:

15,872 mm³

Step-by-step explanation:

given:

A small square pyramid of height 6 cm was removed from the top of a large square pyramid of height 12cm forming the solid shown.

Find:

the exact volume of the solid

solution:

volume of square base pyramid = (base area)² * h/3

where total h = 12 cm

height of top pyramid (ht)= 6 cm

height of bottom pyramid (hb) = 6 cm

bottom volume = total volume - the volume on top

so,

total volume = 1/3 (base area)² h

= 1/3 (8*8)² * 12

= 16,384 mm³

volume on top = 1/3 (top base area)² h

= 1/3 (4*4)² * 6

= 512 mm³

finally: get the bottom volume:

bottom volume = total volume - the volume on top

bot. vol = 16,384 mm³ - 512 mm³

= 15,872 mm³

therefore,

the volume of the cut pyramid base = 15,872 mm³