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Digital SAT Math Practice Questions -Advanced : Area and volume

Digital SAT Math Practice Questions -Advanced : Area and volume - New Syllabus

DSAT MAth Practice questions – all topics

  • Geometry and Trigonometry Weightage: 15% Questions: 5-7
    • Area and volume
    • Lines, angles, and triangles
    • Right triangles and trigonometry
    • Circles

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Question Hard

Rectangular garden with paved path

The rectangular garden shown has a width of 50 feet and a length of 45 feet and is surrounded by a paved path with a uniform width of \(x\) feet. If the combined area of the garden and the paved path is 2646 square feet, what is the value of \(x\) ?

A) 1

B) 2

C) 3

D) 4

▶️ Answer/Explanation
Solution

Answer: 2

Total Area of rectangle will be length \(\times\) breadth \(= 546\)

As \(\mathrm{x}\) denotes distance which cant be negative.

Question Hard

The figure shown is a right circular cylinder with a radius of \( r \) and height of \( h \). A second right circular cylinder (not shown) has a volume that is 392 times as large as the volume of the cylinder shown. Which of the following could represent the radius \( R \), in terms of \( r \), and the height \( H \), in terms of \( h \), of the second cylinder?

Right Circular Cylinder

A) \( R = 8r \) and \( H = 7h \)

B) \( R = 8r \) and \( H = 49h \)

C) \( R = 7r \) and \( H = 8h \)

D) \( R = 49r \) and \( H = 8h \)

▶️ Answer/Explanation
Solution

Ans: C

Volume of first cylinder = \( \pi r^2 h \). Second cylinder volume = \( \pi R^2 H = 392 \pi r^2 h \).

So, \( R^2 H = 392 r^2 h \). Check options:

A) \( (8r)^2 (7h) = 64r^2 \cdot 7h = 448r^2 h \) (incorrect).

B) \( (8r)^2 (49h) = 64r^2 \cdot 49h = 3136r^2 h \) (incorrect).

C) \( (7r)^2 (8h) = 49r^2 \cdot 8h = 392r^2 h \) (correct).

D) \( (49r)^2 (8h) = 2401r^2 \cdot 8h = 19208r^2 h \) (incorrect).

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