The height of a square pyramid is 12cm slant height 15cm calculate total surface area and volume?
Answers
Answer:
Step-by-step explanation:
1296
c
m
3
Explanation:
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The volume of a square pyramid is given by:
V
=
1
3
a
2
h
Where
a
is the side of a square and
h
is the height of the pyramid.
Looking at the diagram. We know the slant height and the height, but we need the length of the base side.
Using Pythagoras' theorem:
15
2
=
12
2
+
(
1
2
a
)
2
15
2
=
12
2
+
1
4
a
2
81
=
1
4
a
2
a
2
=
324
a
=
√
324
=
18
Volume of pyramid:
V
=
1
3
(
18
)
2
(
12
)
=
1296
c
m
3
Answer:
864cm2 and 1296cm3
Step-by-step explanation:
{Note: root of 2 is written as 2}
height =12 cm. slant height = 15 cm
a = 2 √ 15 2 − 12 2 = 2 x 9 = 18 cm2
Total surface area = base- area + curved surface area
= (18)2 + 2 × 18 × 15 = 324 + 540 = 864 cm2
Volume = 1/3 (18)2 x 12 = 1296 cm3
Hope it will help you :)