We read your photo as:

Calculate the volume of these solids (cone, cube, cuboid, cylinder)?

Mathematics

ScanSolve AI Answer

Answers

7 parts
a

128.33 cm3\text{128.33 cm}^3

b

125 cm3\text{125 cm}^3

c

64 cm3\text{64 cm}^3

d

1540 cm3\text{1540 cm}^3

31

616 cm2\text{616 cm}^2

32

208 cm2\text{208 cm}^2

10

1232 cm2\text{1232 cm}^2

Step-by-step solution

14 steps

Here are the solutions to the remaining questions.

Part 20

Calculate the volume of these solids (8 marks)

Part a

128.33 cm3\text{128.33 cm}^3

Cone

  1. Identify the given dimensions.

    Radius r=3.5 cmr = 3.5\, \text{cm}
    Height h=10 cmh = 10\, \text{cm}

  2. Use the formula for the volume of a cone.

    V=13πr2hV = \frac{1}{3}\pi r^2 h

    Using π=227\pi = \frac{22}{7}:

    V=13×227×(3.5 cm)2×10 cmV = \frac{1}{3} \times \frac{22}{7} \times (3.5\, \text{cm})^2 \times 10\, \text{cm} V=13×227×12.25 cm2×10 cmV = \frac{1}{3} \times \frac{22}{7} \times 12.25\, \text{cm}^2 \times 10\, \text{cm} V=13×22×1.75 cm2×10 cmV = \frac{1}{3} \times 22 \times 1.75\, \text{cm}^2 \times 10\, \text{cm} V=13×385 cm3V = \frac{1}{3} \times 385\, \text{cm}^3 V=128.33 cm3V = 128.33\, \text{cm}^3

    The volume of the cone is 128.33 cm3\boxed{\text{128.33 cm}^3}.

Part b

125 cm3\text{125 cm}^3

Cube

  1. Identify the given dimension.

    Side length s=5 cms = 5\, \text{cm}

  2. Use the formula for the volume of a cube.

    V=s3V = s^3 V=(5 cm)3V = (5\, \text{cm})^3 V=125 cm3V = 125\, \text{cm}^3

    The volume of the cube is 125 cm3\boxed{\text{125 cm}^3}.

Part c

64 cm3\text{64 cm}^3

Cuboid

  1. Identify the given dimensions.

    Length l=8 cml = 8\, \text{cm}
    Width w=4 cmw = 4\, \text{cm}
    Height h=2 cmh = 2\, \text{cm}

  2. Use the formula for the volume of a cuboid.

    V=l×w×hV = l \times w \times h V=8 cm×4 cm×2 cmV = 8\, \text{cm} \times 4\, \text{cm} \times 2\, \text{cm} V=64 cm3V = 64\, \text{cm}^3

    The volume of the cuboid is 64 cm3\boxed{\text{64 cm}^3}.

Part d

1540 cm3\text{1540 cm}^3

Cylinder

  1. Identify the given dimensions.

    Radius r=7 cmr = 7\, \text{cm}
    Height h=10 cmh = 10\, \text{cm}

  2. Use the formula for the volume of a cylinder.

    V=πr2hV = \pi r^2 h

    Using π=227\pi = \frac{22}{7}:

    V=227×(7 cm)2×10 cmV = \frac{22}{7} \times (7\, \text{cm})^2 \times 10\, \text{cm} V=227×49 cm2×10 cmV = \frac{22}{7} \times 49\, \text{cm}^2 \times 10\, \text{cm} V=22×7 cm2×10 cmV = 22 \times 7\, \text{cm}^2 \times 10\, \text{cm} V=1540 cm3V = 1540\, \text{cm}^3

    The volume of the cylinder is 1540 cm3\boxed{\text{1540 cm}^3}.

Part 31

616 cm2\text{616 cm}^2

Find the Surface area of a Sphere of radius 7cm. 2 marks

  1. Identify the given dimension.

    Radius r=7 cmr = 7\, \text{cm}

  2. Use the formula for the surface area of a sphere.

    A=4πr2A = 4\pi r^2

    Using π=227\pi = \frac{22}{7}:

    A=4×227×(7 cm)2A = 4 \times \frac{22}{7} \times (7\, \text{cm})^2 A=4×227×49 cm2A = 4 \times \frac{22}{7} \times 49\, \text{cm}^2 A=4×22×7 cm2A = 4 \times 22 \times 7\, \text{cm}^2 A=88×7 cm2A = 88 \times 7\, \text{cm}^2 A=616 cm2A = 616\, \text{cm}^2

    The surface area of the sphere is 616 cm2\boxed{\text{616 cm}^2}.

Part 32

208 cm2\text{208 cm}^2

Find the Surface of a Cuboid. 8cm x 6cm x 4cm. 2 marks

  1. Identify the given dimensions.

    Length l=8 cml = 8\, \text{cm}
    Width w=6 cmw = 6\, \text{cm}
    Height h=4 cmh = 4\, \text{cm}

  2. Use the formula for the surface area of a cuboid.

    A=2(lw+lh+wh)A = 2(lw + lh + wh) A=2((8 cm×6 cm)+(8 cm×4 cm)+(6 cm×4 cm))A = 2((8\, \text{cm} \times 6\, \text{cm}) + (8\, \text{cm} \times 4\, \text{cm}) + (6\, \text{cm} \times 4\, \text{cm})) A=2(48 cm2+32 cm2+24 cm2)A = 2(48\, \text{cm}^2 + 32\, \text{cm}^2 + 24\, \text{cm}^2) A=2(104 cm2)A = 2(104\, \text{cm}^2) A=208 cm2A = 208\, \text{cm}^2

    The surface area of the cuboid is 208 cm2\boxed{\text{208 cm}^2}.

Part 10

1232 cm2\text{1232 cm}^2

A hemisphere bowl of radius 14cm is to be painted.

Assuming the question asks for the surface area of the outer curved surface of the open hemisphere bowl.

  1. Identify the given dimension.

    Radius r=14 cmr = 14\, \text{cm}

  2. Use the formula for the curved surface area of a hemisphere.

    A=2πr2A = 2\pi r^2

    Using π=227\pi = \frac{22}{7}:

    A=2×227×(14 cm)2A = 2 \times \frac{22}{7} \times (14\, \text{cm})^2 A=2×227×196 cm2A = 2 \times \frac{22}{7} \times 196\, \text{cm}^2 A=2×22×28 cm2A = 2 \times 22 \times 28\, \text{cm}^2 A=44×28 cm2A = 44 \times 28\, \text{cm}^2 A=1232 cm2A = 1232\, \text{cm}^2

    The surface area to be painted is 1232 cm2\boxed{\text{1232 cm}^2}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QCalculate the height and volume of a solid composed of a cone, cylinder, and hemisphere.QCalculate the volume of a cone with radius 3.5 cm and height 10 cm, a cube with side 5 cm, and a…QCalculate the volumes of the following shapes: a) Rectangular prism, b) Cylinder, c) Triangular…QFind the volume and surface area of a sphere with radius 3.5 cm and a cone with radius 7 cm and…QCalculate the volume of cuboids given different sets of dimensions or volume.
Browse by topic:Geometry
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp