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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=7extcm and height h=10extcm.
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=1540extcm3
A is correct because the product of the base area 154extcm2 and the height 10extcm results in a total volume of 1540extcm3.
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.