A conical heap is formed when a farmer pours food grains on the ground. The slant height of the heap is 35cm. the circumference of the base is 132cm. What amout of tarpaulin is needed to cover the grains?
Answers
in the cone
slant height = 35 cm
perimeter of the circle = 132 cm
2πr = 132
r = 132 × 7/22 ×2
r = 21 cm
CSA of the cone = πrl
= 22/7 ×21 ×35
= 2310 cm²
∴to cover the grains we need 2310 cm² tarpaulin
Answer:
6,462.12 cm³
Step-by-step explanation:
Given:
Circumference of thebase= 132 cm
slant height = 35 cm
We need to get the volume of the cone. We need the radius of the cone.
Circumference = 2 π r
r = circumference / 2π
r = 132 cm / 2 * 3.14
r = 132 cm / 6.28
r = 21 cm
Volume of the cone = 1/3 π r² √l² - r²
V = 1/3 * 3.14 * (21cm)² * √(35² - 21²)
V = 1/3 * 3.14 * 441cm² * √1225-441cm
V = 461.58cm² * √784cm
V = 461.58cm² * 28cm
V = 12,924.24 cm³
Surface area of the cone to know the measurement of the tarpaulin needed.
Surface area = π r l + πr²
SA = 3.14 * 21cm * 35cm + 3.14 (21cm)²
SA = 2,307.9 cm² + 3.14 (441cm²)
SA = 2,307.9 cm² + 1,384.74 cm²
SA = 3,692.64 cm²
Tarpaulin = 3,692.64 cm²
Half of the grain given to orphanage = 12,924.24 cm³ ÷ 2 = 6,462.12 cm³
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