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Math  /  Geometry

Question5. A soft drink can has a diameter of 6 cm and a height of 11.5 cm . (a) What is its volume? (b) What is its surface area?

Studdy Solution

STEP 1

1. The soft drink can is a cylinder.
2. The diameter of the cylinder is 6 6 cm, which implies the radius is 3 3 cm.
3. The height of the cylinder is 11.5 11.5 cm.

STEP 2

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

STEP 3

Recall the formula for the volume of a cylinder:
V=πr2h V = \pi r^2 h
where r r is the radius and h h is the height.

STEP 4

Substitute the given values into the volume formula:
V=π(3 cm)2(11.5 cm) V = \pi (3 \text{ cm})^2 (11.5 \text{ cm})

STEP 5

Calculate the volume:
V=π(9 cm2)(11.5 cm) V = \pi (9 \text{ cm}^2) (11.5 \text{ cm}) V=π(103.5 cm3) V = \pi (103.5 \text{ cm}^3) V≈325.95 cm3 V \approx 325.95 \text{ cm}^3

STEP 6

Recall the formula for the surface area of a cylinder:
SA=2πr(h+r) SA = 2\pi r(h + r)

STEP 7

Substitute the given values into the surface area formula:
SA=2π(3 cm)(11.5 cm+3 cm) SA = 2\pi (3 \text{ cm})(11.5 \text{ cm} + 3 \text{ cm})

STEP 8

Calculate the surface area:
SA=2π(3 cm)(14.5 cm) SA = 2\pi (3 \text{ cm})(14.5 \text{ cm}) SA=2π(43.5 cm2) SA = 2\pi (43.5 \text{ cm}^2) SA≈273.56 cm2 SA \approx 273.56 \text{ cm}^2
The volume of the can is approximately:
325.95 cm3 \boxed{325.95 \text{ cm}^3}
The surface area of the can is approximately:
273.56 cm2 \boxed{273.56 \text{ cm}^2}

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