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Math  /  Geometry

QuestionFind the volume and Surface Area 380.

Studdy Solution

STEP 1

1. The cone has a radius r=7 r = 7 cm.
2. The height h=18 h = 18 cm.
3. The slant height l=20 l = 20 cm.
4. Use π≈3.14159\pi \approx 3.14159.

STEP 2

1. Calculate the volume of the cone.
2. Calculate the surface area of the cone.

STEP 3

Recall the formula for the volume of a cone:
V=13πr2h V = \frac{1}{3} \pi r^2 h

STEP 4

Substitute the given values into the volume formula:
V=13π(7 cm)2(18 cm) V = \frac{1}{3} \pi (7 \text{ cm})^2 (18 \text{ cm})

STEP 5

Calculate the volume:
V=13π(49 cm2)(18 cm) V = \frac{1}{3} \pi (49 \text{ cm}^2) (18 \text{ cm}) V=13π(882 cm3) V = \frac{1}{3} \pi (882 \text{ cm}^3) V=294π cm3 V = 294 \pi \text{ cm}^3 V≈294×3.14159 cm3 V \approx 294 \times 3.14159 \text{ cm}^3 V≈923.63 cm3 V \approx 923.63 \text{ cm}^3

STEP 6

Recall the formula for the surface area of a cone:
SA=πr(r+l) SA = \pi r (r + l)

STEP 7

Substitute the given values into the surface area formula:
SA=π(7 cm)(7 cm+20 cm) SA = \pi (7 \text{ cm}) (7 \text{ cm} + 20 \text{ cm})

STEP 8

Calculate the surface area:
SA=π(7 cm)(27 cm) SA = \pi (7 \text{ cm}) (27 \text{ cm}) SA=189π cm2 SA = 189 \pi \text{ cm}^2 SA≈189×3.14159 cm2 SA \approx 189 \times 3.14159 \text{ cm}^2 SA≈593.76 cm2 SA \approx 593.76 \text{ cm}^2
The volume of the cone is approximately:
923.63 cm3 \boxed{923.63 \text{ cm}^3}
The surface area of the cone is approximately:
593.76 cm2 \boxed{593.76 \text{ cm}^2}

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