# GRE® Quant Practice | Geometry

###### Surface Area & Volume | Sector of circle recast into Cone

This GRE quant practice question is a geometry - solid geometry problem solving question. Computing the volume of a right circular cone obtained by recasting or rotating a sector of a circle.

Question 1 : A sector of a circle of radius 5 cm is recast into a right circular cone of height 4 cm. What is the volume of the resulting cone?

1. 12 π cm3
2. 100 π cm3
3. 33 π cm3
4. 32 π cm3
5. 4 π cm3

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### Explanatory Answer | GRE Geometry Practice Question 1

#### Step 1 of solving this question: Compute Slant Height of the Resulting Cone

The sector of a circle with radius 5 cm.
When recast into a right-circular cone of height 4 cm the sector will appear as shown in the diagram.
The radius of the sector will be the slant height of the cone.
So, the slant height of the cone is 5 cm.

#### Step 2 of solving this question: Compute the base radius of the cone

The base radius, slant height, and the height of the cone form a right triangle, with the slant height being the hypotenuse of the triangle.
Slant height of the cone, which is the hypotenuse of the triangle is 5 cm.
The height of the cone, which is one of the perpendicular sides of the triangle is 4 cm.
By Pythagoras theorem, we can compute the radius r =$$sqrt{$$text{Slant Height}$^2 -$$text{Height})^2}) r = $\sqrt{$5$^2 -(4)^2}) = $$sqrt{25 − 16}$ = $\sqrt{9}$ → r = 3 cm #### Step 3 of solving this question: Compute the Volume of the Cone Volume of a right circular cone = $\frac{1}{3}$ π r2 h radius = 3 cm and height = 4 cm So, volume = $\frac{1}{3}$ π × 32 × 4 = 12 π cm3 ##### Choice A is the correct answer ###### GRE Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! ###### Already have an Account? ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 48/1 Ramagiri Nagar Velachery Taramani Link Road., Velachery, Chennai 600 042. India ##### How to reach Wizako? Phone:$91) 44 4500 8484
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