Surface Area
A square pyramid has a side base of 15m. Its triangles' height are all 9m. What is its surface area? (Hint: Area of a triangle = ½*b*h and Area of a rectangle = l*w)
Area of the base = l*w =15m x 15m = 225m2
Area of the triangles = 4*1/2*b*h
= 4*1/2*15m*9m
= 270m2
Total Area = 270m2+225m2 = 495m2
A rectangular prism has side lengths of 7m, 8.4m, and 8.75m. What is its volume? (Hint: volume of a rectangular prism = l*w*h)
v = 7m*8.4m*8.75m = 514.5m3
A cereal box has a width of 5 inches, a length of 8 inches, and a height of 12 inches. What is its surface area? (Hint: Area of a rectangle = l*w*h)
SA = 2(5in*8in) + 2(5in*12in) + 2(8in*12in)
= 80in2 + 120in2 + 192in2
= 392in2
A rectangular prism has side lengths of 7m, 8.4m, and 8.75m. What is the surface area? (Hint: Area of a rectangle = l*w)
SA= 2(7m*8.4m)+2(8.4m*8.75m)+2(7m*8.75m) =387.1m2
The rectangular prism has side lengths of 4ft, 2.3ft, and 6.25ft. What is the volume of the rectangular prism? (Hint: volume of a rectangular prism = l*w*h)
V = 4ft*2.3ft*6.25ft =57.5ft3
A rectangular prism has a volume of 6336cm3. It also has a width of 12cm and a height of 16cm. What is the length of the rectangular prism? (Hint: Volume of a rectangular prism = l*w*h)
V = 6336cm3 = l*12cm*16cm
6336cm3 = l*192cm2
6336cm3/192cm2= l*192cm2/192cm2
33cm = l
The rectangular prism has side lengths of 4ft, 2.3ft, and 6.25ft. What is the surface area of the rectangular prism? (Hint: Area of a rectangle = l*w)
SA = 2(4ft*2.3ft)+2(4ft*6.25ft)+2(2.3ft*6.25ft)
= 97.15ft2
The volume inside a rectangular storage room is 2,940 cubic feet. The room is 12 feet high. Find the area of the floor? (Hint: Volume of a rectangular prism=B*h or l*w*h)
V = 2940ft3 = B*12ft
2940ft3/12ft = (12ft/12ft)*B
245ft = B
Lily is wrapping a triangular prism box. The triangular base has a base of 8in, a height of 6in, and a hypotenuse (3rd side) of 10in. The height of the box is 4in. If wrapping paper is $0.02 per square inch, how much will Lily spend on wrapping paper? (Hint: Area of a rectangle = l*w and Area of a triangle = 1/2*b*h)
SAtriangles = 2(1/2*8in*6in) = 48in2
SArectangle1 = 4in*10in = 40in2
SArectangle2 = 4in*6in = 24in2
SArectangle3 = 4in*8in = 32in2
Total SA = 48in2 + 40in2 + 24in2 + 32in2 = 144in2
Total Price =144in2 * $0.02/in2 = $2.88
An aquarium holds 11.25 cubic feet of water, and is 2.5 feet long and 1.5 feet wide. What is its depth? (Hint: Volume of a rectangular prism = l*w*h)
V = 11.25ft3 = 2.5ft*1.5ft*h
11.25ft3 = 3.75ft2*h
11.25ft3/3.75ft2 = (3.75ft2/3.75ft2)*h
3ft = h
A fancy teabag comes in a square pyramid box. The box is a square pyramid whose base is 1.5 inches on each side. The height of each triangular face of the pyramid is 0.75 inches. How much cardstock was used to make the box? (Hint: Area of a rectangle = l*w and Area of a triangle = 1/2*b*h)
SAbase = 1.5in*1.5in = 2.25in2
SAtriangles = 4(1/2*1.5in*0.75in) = 2.25in2
Total SA = 2.25in2 + 2.25in2 = 4.5in2
A bathtub in the shape of a rectangular prism is 5 feet long, 3 1/2 feet wide, and 4 1/4 feet high. How much water could the tub hold? (Hint: Volume of a rectangular prism = l*w*h)
v = 5ft*3.5ft*4.25ft = 74.375ft3