Câu hỏi
Daysat Section:[SC 2405]OFFICIAL MATH TEST 3 - MODUL 00:03:44 uestion 22 of 22 A big candle is made up of a pyramid with a slant height of 39 cm attached to a cuboid with a square base of sides a cm and a height of 70 cm. Calculate the length of square if the volume of the candle is 738 litters.
Giải pháp
4.5
(110 Phiếu)
Vĩnh Quang
thầy · Hướng dẫn 5 năm
Trả lời
To solve this problem, we need to find the length of the square base of the cuboid part of the candle.Given information:- The candle is made up of a pyramid with a slant height of 39 cm and a cuboid with a square base.- The height of the cuboid is 70 cm.- The volume of the candle is 73.8 liters.Step 1: Convert the volume from liters to cubic centimeters.1 liter = 1000 cubic centimetersVolume of the candle = 73.8 liters = 73,800 cubic centimetersStep 2: Calculate the volume of the pyramid.Volume of a pyramid = (1/3) × base area × heightLet's denote the length of the square base as 'a' cm.Volume of the pyramid = (1/3) × a^2 × 39Step 3: Calculate the volume of the cuboid.Volume of a cuboid = base area × heightVolume of the cuboid = a^2 × 70Step 4: Set the total volume of the candle equal to the sum of the volumes of the pyramid and the cuboid.Total volume = Volume of the pyramid + Volume of the cuboid73,800 = (1/3) × a^2 × 39 + a^2 × 70Step 5: Solve the equation for the length of the square base 'a'.73,800 = (1/3) × a^2 × 39 + a^2 × 7073,800 = 13 × a^2 + 70 × a^273,800 = 83 × a^2a^2 = 73,800 / 83a = √(73,800 / 83)a ≈ 94.5 cmTherefore, the length of the square base of the cuboid part of the candle is approximately 94.5 cm.