Surface Area
Solids of revolution
Volume
Similar figures
Potpourri
100
What is the surface area of a cube with the side length 4cm?
96 cm2
100
What 2D figure, when rotated about the x- or y-axis, creates a cylinder?
A rectangle (or square)
100
Bob's rectangular prism fish tank has a volume of 300 cm3. The length is 5 cm. The width is 6 cm. What is height?
10 cm
100
Two similar cones have a similarity ratio of 2:3. What's the ratio of their volumes?
8:27
100
When a plane cuts a sphere in half, the resulting two half-spheres are known as _________
Hemispheres
200
What's the difference between surface area and lateral area?
Surface area includes the bases, lateral area is just the sides of the figure
200
A right triangle with base 2m and height 4m is rotated about the y-axis. What is the volume of the resulting solid? Round your answer to the nearest tenth.
16.8m3
200
Find the volume of a square pyramid with a base length 24ft and height 16ft.
3072 ft2
200
Two similar spheres have a surface area ratio of 1:9. The radius of the larger sphere is 30 miles. What's the radius of the smaller sphere?
10 miles
200
Find the surface area of this weird thing
1620ft2
300
What figure does this net make?
Square pyramid
300
A cylinder with a diameter 12 and height 9 is created by rotating a rectangle about the y-axis. What's the area of the rectangle?
9 units tall, 6 units wide -> A = 54 square units
300
How many cones of radius r and height 2r fit into a sphere of radius r?
2 of em!
300
Are the cylinders similar? If so, give the ratio of their volumes.
Not similar!!! 14/10 != 42/35
300
Solve for x: 10x + x2 = 3000
x = 50, -60
400
Find the surface area of a cylinder with diameter 14 and height 15 cm. Keep your answer in terms of pi.
308pi cm2
400
Find the volume of the solid that results from rotating the figure below around the y-axis (be careful!!!)
r = 3, round your answer to the nearest tenth.
56.5 un3
400
Find the volume of a regular hexagonal prism with a side length of 6 mm and a height of 10 mm. Keep your answer in simplest radical form.
540sqrt(3) mm3
400
Two similar cubes have volumes of 128 and 250. What is their surface area ratio?
16:25
400
I store my prized bowling ball (radius of 4 in) in a cubic box with side length of 8 in. How much empty space is in the box when my bowling ball is inside it? Round your answer to the nearest tenth.
83 - 4/3pi(4^3) = 243.9 in3
500
Find the surface area of a triangular pyramid where all faces are equilateral triangles with base 5 and height 2.
20 square centimeters
500
Find the surface area of the 3D figure created when the semicircle pictured below is rotated around the x-axis. Keep your answer in terms of pi.
16pi units2
500
A sphere has a surface area of 144π square centimeters (that's a pi... sorry)
What's its volume (in terms of pi)?
288pi cm3
500
The first-period-sized cardboard box of candy has dimensions 3x6x8 inches. The sixth-period-sized box is similar, but larger, with a side ratio of 1:2. How much more cardboard is used in the 6th period box than in the 1st period box?
1st period: 180 sq inches
6th period: 720 sq inches
6th period uses 540 sq inches more cardboard!
500
A pill is in the shape of a cylinder with two half-sphere ends. The radius of the cylinder (and the half-spheres) is 3mm and the length of the entire pill is 36mm. To the nearest cubic mm, what's the volume of the pill?
961mm3
(it's a cylinder with r = 3 and height = 30 combined with a sphere of r = 3)