Your city council has decided to build a cone shaped reservoir. The plan that was given to the building…

Question

Your city council has decided to build a cone shaped reservoir. The plan that was given to the building contractor indicated that the top diameter of the reservoir must be 50m. The depth of the reservoir is indicated at 30m. 1. What volume of water can be stored in the reservoir? II. What is the surface area of the wall of the cone?

ScanSolve AI Tutor · Accepted Answer

Question I: What volume of water can be stored in the reservoir? Step 1: Formula for the volume of a cone. V = 1/3 π r² h; Top diameter = 50 m, so radius r = 25 m. Depth h = 30 m. Step 2: Substitute the values. V = 1/3 π (25)² (30); = 1/3 π (625) (30); = 1/3 π (18750); = 6250 π; Volume = 6250 π m³. 6250π m³ Question II: What is the surface area of the wall of the cone? Step 1: Slant height l. l = √(r² + h²); = √(25² + 30²); = √(625 + 900); = √(1525); = √(25 × 61); = 5√(61); Slant height = 5√(61) m. Step 2: Lateral surface area of the cone. A = π r l; A = π (25) (5√(61)); = 125 π √(61); Surface area = 125 π √(61) m². 125π√(61) m²

Answers

Step-by-step solution

Part i· 2 steps

Formula for the volume of a cone.

Substitute the values.

Part ii· 2 steps
$125\pi\sqrt{61} \text{ m}^2$

Slant height $l$ .

Lateral surface area of the cone.

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