Introduction to Torus help with math:
This article deals with the torus and how the math formula helps to find the torus volume and surface area. Torus is the three dimensional ring shaped surface that is produced by rotating a circle around an axis. Here the axis will never intersect the circle. The cross section of the torus looks like a ring.
Math formula:
With the help of math formula we can find the volume and surface area.
For volume:
When radius is given:
Volume of the torus =` 2*pi^2*R*r^2` cubic units
R is the large radius.
r is the small radius.
When the diameter is given:
Volume of the torus = `((pi^2*D*d^2)/4)` cubic units
D is the large diameter
d is the small diameter
For surface area:
When radius is given:
Surface area of the torus = `4*pi^2*R*r` square units
R is the large radius.
r is the small radius.
When the diameter is given:
Surface area of the torus = `(pi^2*D*d)` cubic units
D is the large diameter
d is the small diameter
Model problems for torus:
Find the volume of the torus with the help of math formula when the larger radius is 10 cm and the smaller radius is 8cm?
Solution:
Larger radius is 10cm.
Smaller radius is 8cm.
When radius is given:
Volume of the torus =` 2*pi^2*R*r^2` cubic units
R is the large radius.
r is the small radius.
= `2 (3.14) ^2*10*8^2`
= `2 (9.8596)*640
= (19.7192)*640
volume of the torus = 12620.29 cm3
2. Find the surface area of the torus with the help of math formula when the larger radius is 10 cm and the smaller radius is 8cm?
Solution:
Larger radius is 10cm.
Smaller radius is 8cm.
When radius is given:
Surface area of the torus = `4*pi^2*R*r ` square units
R is the large radius.
r is the small radius.
= `4 (3.14) ^2*10*8`
= `4 (9.8596)*80`
= (39.4384)*80
surface area of the torus = 3155.072 cm2
3.Find the surface area of the torus with the help of math formula when the larger diameter is 20 cm and the smaller diameter is 10cm?
Solution:
Larger diameter is 20cm.
Smaller diameter is 10cm.
When the diameter is given:
Surface area of the torus = `(pi^2*D*d) ` cubic units
D is the large diameter
d is the small diameter
= (3.14)^2* (20) (10)
= 9.8596 (200)
surface area of the torus = 1971.92 cm2
This article deals with the torus and how the math formula helps to find the torus volume and surface area. Torus is the three dimensional ring shaped surface that is produced by rotating a circle around an axis. Here the axis will never intersect the circle. The cross section of the torus looks like a ring.
Math formula:
With the help of math formula we can find the volume and surface area.
For volume:
When radius is given:
Volume of the torus =` 2*pi^2*R*r^2` cubic units
R is the large radius.
r is the small radius.
When the diameter is given:
Volume of the torus = `((pi^2*D*d^2)/4)` cubic units
D is the large diameter
d is the small diameter
For surface area:
When radius is given:
Surface area of the torus = `4*pi^2*R*r` square units
R is the large radius.
r is the small radius.
When the diameter is given:
Surface area of the torus = `(pi^2*D*d)` cubic units
D is the large diameter
d is the small diameter
Model problems for torus:
Find the volume of the torus with the help of math formula when the larger radius is 10 cm and the smaller radius is 8cm?
Solution:
Larger radius is 10cm.
Smaller radius is 8cm.
When radius is given:
Volume of the torus =` 2*pi^2*R*r^2` cubic units
R is the large radius.
r is the small radius.
= `2 (3.14) ^2*10*8^2`
= `2 (9.8596)*640
= (19.7192)*640
volume of the torus = 12620.29 cm3
2. Find the surface area of the torus with the help of math formula when the larger radius is 10 cm and the smaller radius is 8cm?
Solution:
Larger radius is 10cm.
Smaller radius is 8cm.
When radius is given:
Surface area of the torus = `4*pi^2*R*r ` square units
R is the large radius.
r is the small radius.
= `4 (3.14) ^2*10*8`
= `4 (9.8596)*80`
= (39.4384)*80
surface area of the torus = 3155.072 cm2
3.Find the surface area of the torus with the help of math formula when the larger diameter is 20 cm and the smaller diameter is 10cm?
Solution:
Larger diameter is 20cm.
Smaller diameter is 10cm.
When the diameter is given:
Surface area of the torus = `(pi^2*D*d) ` cubic units
D is the large diameter
d is the small diameter
= (3.14)^2* (20) (10)
= 9.8596 (200)
surface area of the torus = 1971.92 cm2
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