Two similar cylindrical cans have heights of 7cm and 21cm, if the smaller holds 250g of sugar, how many kg of sugar will the larger one hold?
0.75
1.5
2.25
3.5
6.75
Explanation
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Step 1: Volume Ratio of the Cans
The heights of the smaller and larger cans are given as
h 1=7cm and
ℎ2=21cm
The ratio of their heights is:
ℎ2:ℎ1
=21/7=3
Since the shapes are similar, the ratio of their volumes is the cube of the height ratio:
Volume of Larger Can/Volume of Smaller Can=
(ℎ2/ℎ1)³=(3/1)³=27
Step 2: Volume of the Larger Can
The smaller can holds 250g
250g of sugar. Let the amount of sugar held by the larger can be x:
𝑥/250=27⇒
𝑥=27×250=6750g
Convert 6750g to kilograms:
6750/1000=6.75kg
Final Answer
The larger can will hold 6.75 kg of sugar.
Correct Option: E. 6.75
Similar= same diameter
250=πr2h ( volume of a cylinder)
r^2= 250/πh
= 11.38
πr^2 h
3.14×11.38×21
750.39 /1000
= 0.75 (A)
Similar= same diameter
250=πr2h ( volume of a cylinder)
r^2= 250/πh
= 11.38
πr^2 h
3.14×11.38×21
750.39 /1000
= 0.75 (A)
250=πr²h
=3.14×r²×7
250=21.98r²
250=22
=11.36
V=πr²h
V=3.14×11.36×21
V=750g
In kg= g÷1000
750g÷1000
=0.75kg
Greetings, The Myschool Team.
The correct answer is A(0.75) and not E(6.75). Concerning similar shapes, the formula quoted is only valid for cubes and spheres. It is only valid for cylinders if both the radius and heights differ but are similar, but in this question that is not the case. The radii were not said to be different, so it can be assumed that they are the same. The heights are 7cm and 21cm. Now,
Area of larger/Area of smaller = πr²×21/πr²×7
= 3:1
Thus, amount held by larger cylinder =
3 × amount held by smaller cylinder
= 3 × 250g
=750g
= 0.75kg
Thus, the correct answer is A(0.75) and not E(6.75). Please the necessary corrections should be made. Thank you.
