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.

To solve this problem, we need to find the length of the square base of the cuboid part of the candle.<br /><br />Given information:<br />- The candle is made up of a pyramid with a slant height of 39 cm and a cuboid with a square base.<br />- The height of the cuboid is 70 cm.<br />- The volume of the candle is 73.8 liters.<br /><br />Step 1: Convert the volume from liters to cubic centimeters.<br />1 liter = 1000 cubic centimeters<br />Volume of the candle = 73.8 liters = 73,800 cubic centimeters<br /><br />Step 2: Calculate the volume of the pyramid.<br />Volume of a pyramid = (1/3) × base area × height<br />Let's denote the length of the square base as 'a' cm.<br />Volume of the pyramid = (1/3) × a^2 × 39<br /><br />Step 3: Calculate the volume of the cuboid.<br />Volume of a cuboid = base area × height<br />Volume of the cuboid = a^2 × 70<br /><br />Step 4: Set the total volume of the candle equal to the sum of the volumes of the pyramid and the cuboid.<br />Total volume = Volume of the pyramid + Volume of the cuboid<br />73,800 = (1/3) × a^2 × 39 + a^2 × 70<br /><br />Step 5: Solve the equation for the length of the square base 'a'.<br />73,800 = (1/3) × a^2 × 39 + a^2 × 70<br />73,800 = 13 × a^2 + 70 × a^2<br />73,800 = 83 × a^2<br />a^2 = 73,800 / 83<br />a = √(73,800 / 83)<br />a ≈ 94.5 cm<br /><br />Therefore, the length of the square base of the cuboid part of the candle is approximately 94.5 cm.