Answer:
(i) 84 cm.
(ii) 5635π cm^2
Step-by-step explanation:
(i)
The volume of the cone = 1/3 π r^2 h
= 1/3 π 35^2 h.
The volume of the hemisphere = 2/3 π 35^3.
As the volume of the cone is 1 1/5 ( = 6/5) times the volume of the hemisphere:
1/3 π 35^2 h = 2/3 π 35^3 * 6/5
h = 2/3 π 35^3 * 6/5 / 1/3 π 35^2
h = 84 cm (answer).
(ii) Surface area of the hemisphere = 2 π * 35^2 = 2450π cm^2.
Surface area of the cone = π r l where l = slant height.
l = √(35^2 + 84^2) = 91 cm.
So the surface area of the cone = 35*91 π = 3185π.
So the total surface area of the solid is 3185π + 2450π
= 5635π cm^2.
Answer:
<h2>Vertex: (4, 12)</h2><h2>Axis of symerty: x = 4</h2><h2>y - inrercept: -4</h2>
Step-by-step explanation:
The vertex form of quadratic function f(x) = ax² + bx + c:
f(x) = a(x - h)² + k
(h, k) - coordinates of a vertex
h = -b/2a
k = f(h)
We have f(x) = -x² + 8x - 4 ⇒ a = -1, b = 8, c = -4.
h = -8/(2 · (-1)) = -8/(-2) = 4
k = f(4) = -4² + 8 · 4 - 4 = -16 + 32 - 4 = 12
Vertex (4, 12)
Axis of symerty = h: x = 4
y - inrercept f(0) = c: -4
Here we have to find the length of arc AB.
Length of an arc = ( central angle/360)×2 πr
= ( 64.6 / 360 ) × 2 × 5 miles × 22 / 7
= 0.179 × 220 miles / 7
= 39.38 miles / 7
= 5.625 miles.
The required answer is 5.625 miles.
In my personal opinion I'd say a gallon, just because when someone asks "How much lemonade is in that pitcher?" I think it's best to say a gallon over 16 cups(:
Answer:
1.344 cubic units
Step-by-step explanation:
Given data
Base edge a= 1.2
Hieght= 2.8
The expression for the volume of a pyramid is
V= a^2h/3
substitute
V= 1.2^2* 2.8/3
V= 1.44*2.8/3
V= 4.032/3
V= 1.34cubic units