4GMAT Diagnostic Test Q15 - GMAT Problem Solving - Solid Geometry

GMAT QUANTITATIVE REASONING

SOLID GEOMETRY –

VOLUME OF CYLINDER

PROBLEM SOLVING

Diagnostic Test

Question

If the base circumference of a cylinder is 88 cm and its

height is 12 cm, what is the volume of the cylinder?

A. 88𝜋 cc

B. 1056 cc

C. 1848 cc

D. 14944 cc

E. 7392 cc

Step 1

Recap of formulas for cylinder

Formula Recap – Right Circular CylinderBase circumference. Curved and total surface area. Volume

Formula Recap – Right Circular CylinderBase circumference. Curved and total surface area. Volume

Base Circumference

2πr

Formula Recap – Right Circular CylinderBase circumference. Curved and total surface area. Volume

Base Circumference

Curved Surface Area

2πr

2πrh

Formula Recap – Right Circular CylinderBase circumference. Curved and total surface area. Volume

Base Circumference

Curved Surface Area

Total Surface Area

2πr

2πrh

2πrh + 2πr2

Formula Recap – Right Circular CylinderBase circumference. Curved and total surface area. Volume

Base Circumference

Curved Surface Area

Total Surface Area

Volume

2πr

2πrh

2πrh + 2πr2

πr2h

Step 2

Compute radius from base circumference;

calculate volume

What is the volume of the cylinder?Base circumference : 88 cm; height: 12 cm

Step 01 : Compute radius from base circumference

What is the volume of the cylinder?Base circumference : 88 cm; height: 12 cm

Base circumference = 2πr = 88 cm

Step 01 : Compute radius from base circumference

What is the volume of the cylinder?Base circumference : 88 cm; height: 12 cm

Base circumference = 2πr = 88 cm

Step 01 : Compute radius from base circumference

i.e., 2 ×227× r = 88 cm

What is the volume of the cylinder?Base circumference : 88 cm; height: 12 cm

Base circumference = 2πr = 88 cm

Step 01 : Compute radius from base circumference

i.e., 2 ×227× r = 88 cm Or r =

88 × 72 ×22 = 14 cm

What is the volume of the cylinder?Base circumference : 88 cm; height: 12 cm

Base circumference = 2πr = 88 cm

Step 01 : Compute radius from base circumference

i.e., 2 ×227× r = 88 cm Or r =

88 × 72 ×22 = 14 cm

Step 02 : Compute volume. r = 14 cm and h = 12 cm

Volume of cylinder = πr2h

What is the volume of the cylinder?Base circumference : 88 cm; height: 12 cm

Base circumference = 2πr = 88 cm

Step 01 : Compute radius from base circumference

i.e., 2 ×227× r = 88 cm Or r =

88 × 72 ×22 = 14 cm

Step 02 : Compute volume. r = 14 cm and h = 12 cm

Volume of cylinder = πr2h Volume =

227×14

2×12

What is the volume of the cylinder?Base circumference : 88 cm; height: 12 cm

Base circumference = 2πr = 88 cm

Step 01 : Compute radius from base circumference

i.e., 2 ×227× r = 88 cm Or r =

88 × 72 ×22 = 14 cm

Step 02 : Compute volume. r = 14 cm and h = 12 cm

Volume of cylinder = πr2h Volume =

227×14

2×12 Volume = 7392 cm3

Volume 7392 cc

What is the volume of the cylinder?Base circumference : 88 cm; height: 12 cm

Base circumference = 2πr = 88 cm

Step 01 : Compute radius from base circumference

i.e., 2 ×227× r = 88 cm Or r =

88 × 72 ×22 = 14 cm

Step 02 : Compute volume. r = 14 cm and h = 12 cm

Volume of cylinder = πr2h Volume =

227×14

2×12 Volume = 7392 cm3

Correct Answer : Choice E

Volume 7392 cc

What is the volume of the cylinder?Base circumference : 88 cm; height: 12 cm

Base circumference = 2πr = 88 cm

Step 01 : Compute radius from base circumference

i.e., 2 ×227× r = 88 cm Or r =

88 × 72 ×22 = 14 cm

Step 02 : Compute volume. r = 14 cm and h = 12 cm

Volume of cylinder = πr2h Volume =

227×14

2×12 Volume = 7392 cm3

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