Prisms
The SA of this cube with a height of 8ft.
Cube has 6 faces.
Area of 1 face is 8 x 8 = 64
64 x 8 = 384
384 ft ^ 2
The lateral surface area with a height of 6 yards and a diameter of 10 yards. Pi = 3.14
PI (d) x h
3.14 (10) x 6
188.4 y^2
Olivia prepared a cake in the shape of a regular square pyramid, which has a base and slant height of 6 inches. She wants to sprinkle chocolate flakes over the lateral faces of the cake. Find the lateral area of the cake.
SA = 1/2 Pl
SA =1/2 (S1+S2+S3+S4) x slant height
SA = 1/2 (24) x 6
SA = 72 units^2
Find the amount of leather needed to cover a ball 22 cm in diameter. Pi = 3.14
Formula: 4(PI)R^2
4(3.14)(11^2)
1519.76cm^2
A desk is 1.5 feet wide and 5 feet long. It is 3 feet above the
floor. What is the volume of space under the desk?
V = L x W x H
22.5 ft^ 3
A landowner digs a 15-meter-deep well with a diameter of 2.8 m. The landowner spreads the dirt dug out of the hole to form a platform 31.5 meters by 6 meters. Find out how much water can fill the well. PI = 3
Fill - means volume
V =Bh
V = Pi x R^2 X h
V = 3 X 1.4 ^ 2 X 15
V = 88.2 m ^ 3
Find the volume of a rectangular pyramid with a height of 20 meters and the sides of the base are 30 meters and 24 meters.
V = 1/3Bh or 1/3 (l x w) x h
V = 1/3 (30 x24) x 20
V = 1/3 (720) x 20
V =240 X 20
V =4800 m ^ 3
Find the volume of a baseball if its diameter is 6.8 cm. Pi = 3
Formula: V =4/3(PI)(R^3)
V = 4/3 (3) (3.4^3)
V = 157. 216 cm ^ 3
A cube is a rectangular prism with the same measurement for
length, width, and height. If a cube is 4 inches tall, what is its volume?
V = l x w x h
V = 64 units ^2
Sophia needs to paint a planter with 20.75 inches diameter and 19 inches in height. Find the lateral area of the planter. Pi = 3.14, round to nearest tenth
Lateral means the bases are removed.
PI (d) x h
Lateral means bases will not be included.
Formula: 2B + Ch ( remove the 2B as bases are not included).
C (circumference) x h is left
circumference is PI x d (diameter)
3.14 x 20.75 x 19
1,237.945
= about 1,237.9 in ^ 2
Find the surface area of a regular pyramid with a slant height of 12 ft and a side of the square of 11 ft.
Formula: B + 1/2 Pl
(LXW) + 1/2 (S1+S2+S3+S4) X SLANT HEIGHT
121 + 1/2 (44) x 12
121 +264
385 ft ^ 3
The human eye is a spherical structure about 22 mm in diameter. Find the surface area of the eye. PI = 3.14
SA= 4 (PI)(R^2)
4 (3.14) (11^2)
1519.76cm ^2
A fish tank is in the shape of a rectangular prism. The height of the tank is 18 in. The width of the tank is 17 in. The length of the tank is 38 in. Find the amount of water the tank can hold to the nearest in.
Step 1: 18 x 17 x 38 or l x w x h
Step 2: 11,628 in^3
A road roller is a vehicle with smooth and heavy rollers for compacting roads and pavement. If one of these rollers has a diameter of 48 inches and is 36 inches in length, then find the area covered by the roller in one full turn. Pi = 3
Formula:
2B (area of a circle) + C (circumference of a circle) x h
Remove bases because it is lateral area
PI (d) X h
3 (48) (36)
5,184
5,184 in ^ 2
The Transamerica Pyramid is the tallest skyscraper in San Francisco. It has a slant height of 856 ft and has a square base of about 145 ft on each side. Find the Surface area of the pyramid. How many miles would this be? (5,280 ft = 1 mile)
SA = B + (1/2)Pl
SA = LXW + 1/2 (S1+S2+S3+S4) + slant height
SA = 21,025 + 1/2 (580) x 856
SA = 21, 025 + 248, 240 = 269, 265 ft ^2
SA = 50.99 m^2
SA = about 60 square miles
The surface area of a sphere is is 682pi sq inches. Find the volume of the sphere. Give answer in PI.
SA = 4 (PI) (R^2)
682PI = 4PI (R^2)
Divide 4pi on both sides based on rules for solving equations.
170.5 = r²
r = √170.5 ≈ 13.06 inches
Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in. by 2 in. and the front and back are 8 in. by 2 in. How much wrapping paper will Chloe need to wrap the present?
Formula: 2 (l x w) + 2(l x h) + 2( w x h)
2 (8 X3) + 2 ( 3X2) + 2 (8X2)
48 + 12 + 32
92 in ^2
A silo is a cylindrical structure commonly used for bulk storage of grain, coal, cement, carbon black, wood chips, or sawdust. The surface of a silo with a diameter of 60 ft and height of 150 ft needs to be painted. Find the area of the silo to the nearest tenth. PI = 3.14
Step 1: find formulas
2B+Ch = 2 (PI x R^2) + PI (d) (h)
2 x (PI X 30^2) + PI (60) (150)
= 5,654.86 + 28,274.33
=33,929.2 ft^2
Amy and Alex are making models for the science project. Both the models are in shapes of square pyramids. The length of the sides of the base for both models is 8 inches. Amy's model is 5 inches tall and Alex's model is 3 inches tall. Find the difference in volumes of the two models. To the nearest whole number.
Formula : 1/3 Bh or 1/3 (LXW) x H
1/3 x 64 x 5 = 106.67
1/3 x 64 x 3 =64
106.67 - 64 = 42.67 or 43
Some racquet balls are sold in cylindrical cans of three balls. Each ball has a diameter of 2.25 inches. The can has a diameter of 2.25 inches and is 6.75 inches tall. Find the volume of the empty space in the can. Pi = 3.14. Round to nearest hundreth.
Volume of a cylinder: Bh or (PI)(r^2) x h
(3.14 X 1.125^2) X 6.75
26.824 OR 26.82
Volume of a sphere: 4/3 PI (R^3)
3{4/3 (3.14) 1.125^3}
17.88
8.94IN^3