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Calculate the volume of a cylinder with radius 7 cm and height 10 cm. (Use ╧А = 22/7)
1540┬аcm3
1440┬аcm3
154┬аcm3
770┬аcm3
1540┬аcm3
Since the radius is 7, the area of the base (╧Аr2) simplifies easily to 22/7imes49=154. Multiplying by height 10 simply adds a zero to get 1540.
Radius r = 7 cm, height h = 10 cm, and value of ╧А = 22/7.
V=╧Аr2h
Since the radius is 7, the area of the base (╧Аr2) simplifies easily to 22/7imes49=154. Multiplying by height 10 simply adds a zero to get 1540.
Students often use the diameter instead of the radius or mistake the surface area formula (2╧Аrh+2╧Аr2) for the volume formula (╧Аr2h).
Identify given variables
Extract the dimensions provided for the cylinder: radius r=7┬аcm and height h=10┬аcm.
r=7,h=10
Apply volume formula
Substitute the values into the formula for the volume of a cylinder V=╧Аr2h.
V=722тАЛimes72imes10
Perform calculation
Simplify the expression by canceling one 7 from the denominator with one 7 in the squared term, then multiply the remaining digits.
V=22imes7imes10=1540┬аcm3
A is correct because the product of the base area 154┬аcm2 and the height 10┬аcm results in a total volume of 1540┬аcm3.
This concept is foundational for 'Surface Area and Volume' problems in competitive exams. Always remember that volume is always measured in cubic units (cm3), which helps eliminate incorrect options in a hurry.