The volume and surface area of a pyramid with a square base of area a2 and height h is given by
V ha
3
2
= and S a 2a h 2 a
2 = + +2 2 ^ h
A pyramid has a square base and a volume of 3 1 y y8 27y 3 2 + + cubic units.
(i) If its height is y , then what polynomial represents the length of a side of the square base ?
(a) 9 3 ^ h y + (b) 9 3 y 2 ^ h +
(c) 3 3 ^ h y + (d) 3 3 y 2 ^ h
pls ans asap
Answers
Answer 1) :-
we have,
→ square base area of pyramid = a²
→ height = h .
so,
→ Volume = (1/3) * Base area * height = (1/3) * a² * h = (a²h)/3
and,
→ Surface area of pyramid (lateral) = Area of 4 isosceles ∆ = a√(a² + 4h²)
also,
→ Total surface are = LSA + Base area = a² + a√(a² + 4h²) = a{a + √(a² + 4h²)} .
Answer 2) :-
→ Volume of square base pyramid = (3y³ + 12y² + 12y) cm³ (not written properly, so i m assuming .)
→ height = y cm .
Let side of square base = a cm .
so,
→ (1/3) * a² * y = (3y³ + 12y² + 12y)
→ (1/3) * a² * y = 3y(y² + 4y + 4)
→ a² = 9(y² + 4y + 4)
→ a² = 9(y + 2)²
→ a² = 3² * (y + 2)²
→ a = 3(y + 2) cm . (Ans.)
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Answer:
Step-by-step explanation:
we have,
→ square base area of pyramid = a²
→ height = h .
so,
→ Volume = (1/3) * Base area * height = (1/3) * a² * h = (a²h)/3
and,
→ Surface area of pyramid (lateral) = Area of 4 isosceles ∆ = a√(a² + 4h²)
also,
→ Total surface are = LSA + Base area = a² + a√(a² + 4h²) = a{a + √(a² + 4h²)} .
Answer 2) :-
→ Volume of square base pyramid = (3y³ + 12y² + 12y) cm³ (not written properly, so i m assuming .)
→ height = y cm .
Let side of square base = a cm .
so,
→ (1/3) * a² * y = (3y³ + 12y² + 12y)
→ (1/3) * a² * y = 3y(y² + 4y + 4)
→ a² = 9(y² + 4y + 4)
→ a² = 9(y + 2)²
→ a² = 3² * (y + 2)²
→ a = 3(y + 2) cm . (Ans.)
Learn more :-
from a solid cylinder whose height is 3.6 cm and diameter 2.1 CM a conical cavity of the same height and the same diamet...
brainly.in/question/24336372
A hemisphere of radius 21 cm is completely filled with milk. There is a hole in
the bottom whose radius is 0.1 cm. If ra...
brainly.in/question/25349591