Similarity with areas and volumes · Short practice
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Recall
Similarity with areas and volumes — objective 1
Maths4U Original · Short practice
Two geometrically similar solids S and T have corresponding lengths 2 cm and 9 cm. S has surface area \(\displaystyle 9 \mathrm{cm}^{2}\) and volume \(\displaystyle 18 \mathrm{cm}^{3}\).
Find the surface-area multiplier from S to T.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Similarity with areas and volumes — objective 1
Maths4U Original · Short practice
Two geometrically similar solids S and T have corresponding lengths 3 cm and 10 cm. S has surface area \(\displaystyle 10 \mathrm{cm}^{2}\) and volume \(\displaystyle 19 \mathrm{cm}^{3}\).
Find the surface-area multiplier from S to T.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Method
Similarity with areas and volumes — objective 2
Maths4U Original · Short practice
Two geometrically similar solids S and T have corresponding lengths 3 cm and 10 cm. S has surface area \(\displaystyle 10 \mathrm{cm}^{2}\) and volume \(\displaystyle 19 \mathrm{cm}^{3}\).
Find the volume multiplier from S to T.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Similarity with areas and volumes — objective 2
Maths4U Original · Short practice
Two geometrically similar solids S and T have corresponding lengths 4 cm and 11 cm. S has surface area \(\displaystyle 11 \mathrm{cm}^{2}\) and volume \(\displaystyle 11 \mathrm{cm}^{3}\).
Find the volume multiplier from S to T.
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Apply
Similarity with areas and volumes — objective 3
Maths4U Original · Short practice
Two geometrically similar solids S and T have corresponding lengths 4 cm and 11 cm. S has surface area \(\displaystyle 11 \mathrm{cm}^{2}\) and volume \(\displaystyle 11 \mathrm{cm}^{3}\).
Find the surface area of T in \(\displaystyle \mathrm{cm}^{2}\).
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Similarity with areas and volumes — objective 3
Maths4U Original · Short practice
Two geometrically similar solids S and T have corresponding lengths 5 cm and 7 cm. S has surface area \(\displaystyle 12 \mathrm{cm}^{2}\) and volume \(\displaystyle 12 \mathrm{cm}^{3}\).
Find the surface area of T in \(\displaystyle \mathrm{cm}^{2}\).
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Check understanding
Similarity with areas and volumes — objective 4
Maths4U Original · Short practice
Two geometrically similar solids S and T have corresponding lengths 5 cm and 7 cm. S has surface area \(\displaystyle 12 \mathrm{cm}^{2}\) and volume \(\displaystyle 12 \mathrm{cm}^{3}\).
Find the volume of T in \(\displaystyle \mathrm{cm}^{3}\).
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.
Fresh review variant
Similarity with areas and volumes — objective 4
Maths4U Original · Short practice
Two geometrically similar solids S and T have corresponding lengths 2 cm and 8 cm. S has surface area \(\displaystyle 5 \mathrm{cm}^{2}\) and volume \(\displaystyle 13 \mathrm{cm}^{3}\).
Find the volume of T in \(\displaystyle \mathrm{cm}^{3}\).
Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.