3) Construct AABC with BC = 4cm, angle B = 75° and AB +AC = 10 cm.
4)A right angled triangle ABC with sides 6cm, 8cm and 10cm
ABC with sides 6cm, 8cm and10cm is revolved about the side of 8 cm
i) Find the volume of the solid generated.
ii) Also find the total surface area of the solid.
5)The dimensions of a cuboid are in the ratio 4: 3:2. If the total surface area of the cuboid is 4212 m.
Find the volume of the cuboid.
Answers
Answer:
Since, the given right angled triangle is revolved about the side 8 cm, it will form a Cone of radius 6cm and height 8cm.
Volume of a cone = 1/3∏r2h = 1/3×3.14×6×6×8 = 301.44 cm3
Curved Surface area of a cone =∏rl .... (i)
We know that,
l2 = r2 + h2 = 62 + 82 = 36 + 64 = 100
→ l = 10 cm
Substitute the value of l in (i), we get
Curved Surface area of a cone = 3.14 × 6 × 10 = 188.4 cm2 .
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Question:
The dimensions of a cuboid are in the ratio 4: 3:2. If the total surface area of the cuboid is 4212 m. Find the volume of the cuboid.
Given:
Dimensions of cuboid = 2:3:4
Total Surface Area = 5200 cm
To Find:
Volume of cuboid = ?
Step-by-step-explanation:
Let
Length = 2x
Breadth = 3x
Height = 4x
➳ TSA of cuboid = 2(lb + bh + hl)
➞ 5200 = 2(2x.3x + 3x.4x + 4x.2x)
➞ 5200 = 2(6x² + 12x² + 8x²)
➞ 5200 = 2(26x²)
➞ 5200 = 52x²
➞ x² = 5200 ÷ 52
➞ x² = 100
➞ x = √100
➞ x = ± 10
Side cannot be negative.
∴ x = 10 cm
Now let's find the sides of the cuboid.
Length = 2x = 2(10) = 20 cm
Breadth = 3x = 3(10) = 30 cm
Height = 4x = 4(10) = 40 cm
For finding Volume,
Volume = Length × Breadth × Height
➪ Volume = 20 × 30 × 40
➪ Volume = 24000 cm³
∴ Volume = 24000 cm³