Answer:
Total surface area = 434 cm²
Total volume = 470 cm³
Step-by-step explanation:
1. The prism can be decomposed into two rectangular prisms which are the bigger rectangular prism and the smaller rectangular prism
✔️Total surface area of the prism = (surface area of the bigger prism - area of the face joined to the smaller prism) + (surface area of the smaller prism - area of the face joined to the bigger prism)
Surface Area of bigger prism = 2(LW + LH + HW)
L = 10 cm
H = 8 cm
W = 9 - 5 = 4 cm
Area of bigger rectangular prism = 2(10*4 + 10*8 + 8*4)
= 304 cm²
Surface area of the smaller prism = 2(LW + LH + HW)
L = 10 cm
H = 3 cm
W = 5 cm
Area of bigger rectangular prism = 2(10*5 + 10*3 + 3*5)
= 190 cm²
Area of the face joining both rectangular prisms = L*W
L = 10 cm
W = 3 cm
Area = 10*3 = 30 cm²
✅total surface area of the prism = (304 - 30) + (190 - 30) = 274 + 160 = 434 cm²
2. Volume of the prism = volume of the bigger rectangular prism + volume of the smaller rectangular prism
✔️Volume of the bigger rectangular prism = L*W*H
L = 10 cm
H = 8 cm
W = 9 - 5 = 4 cm
Volume = 10*8*4 = 320 cm³
✔️✔️Volume of the bigger rectangular prism = L*W*H
L = 10 cm
H = 3 cm
W = 5 cm
Volume = 10*3*5 = 150 cm³
✅Total Volume of the prism = 320 + 150 = 470 cm³
Answer:
x is 30° and y is 150°
Step-by-step explanation:
x is 30° and y is 150°. These facts stem from the horizontal lines all being parallel and sharing a single transversal which creates the angles shown in this illustration.
Answer:
13
Step-by-step explanation:
Draw a picture!
You have a right triangle with legs of 5 and 12.
By the Pythagorean Theorem, the hypotenuse is √(5²+12²) = 13
Answer:
radius = 6 cm
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = 
πr³ ← r is the radius
Given V = 288π, then
πr³ = 288π
Multiply both sides by 3 to clear the fraction
4πr³ = 864π ( divide both sides by 4π )
r³ = 216 ( take the cube root of both sides )
r = ![\sqrt[3]{216}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B216%7D)
= 6
Thus the radius of the sphere is 6 cm
Answer:
4g+4.25
25
Step-by-step explanation:
He doesn't have more than $25
