The two cones are similar. (a) Write down the value of l. (b) When full, the larger cone contains 172 cm3 of water. How much wat
er does the smaller cone contain when it isfull?
1 answer:
Answer/Step-by-step explanation:
a. Since both cones, as shown in the figure attached below, are similar, 11/8 = l/4
Cross multiply to find l
4*11 = 8*l
44 = 8l
l = 44/8
l = 5.5cm
b. Given the slant height and diameter of cone, volume of cone can be calculated using the formula ⅓πr²*√(l² - r²)
Where, r = diameter ÷ 2 = 4/2 = 2cm
l = 5.5cm
Volume of smaller cone = ⅓*3.142*2²*√(5.5² - 2²)
= ⅓*3.142*4*√30.25 - 4)
= ⅓*12.568*√26.25
= ⅓*12.568*5.124
= 64.40/3
Volume of small cone ≈ 21.5 cm³
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