Composite 3D Figures

Grade 10·20 problems·~35 min·ACT Math·topic·act-geo-3d-composite

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Recall / Warm-Up

What is the volume of a cylinder with radius 5 cm and height 8 cm? Leave your answer in terms of $\pi$ .

$40\pi$ cm³

$80\pi$ cm³

$200\pi$ cm³

$400\pi$ cm³

What is the lateral surface area of a cylinder with radius 3 cm and height 10 cm?

$30\pi$ cm²

$60\pi$ cm²

$78\pi$ cm²

$90\pi$ cm²

What is the volume of a hemisphere with radius 6 cm? Express your answer in terms of $\pi$ .

Fluency Practice

$A cone of height 4 m and radius 5 m sitting on top of a cylinder of height 12 m and radius 5 m, with labeled dimensions.$

A solid is formed by placing a cone (radius 5 m, height 4 m) on top of a cylinder (radius 5 m, height 12 m). What is the total volume? Express your answer in terms of $\pi$ .

$A hemisphere of radius 4 cm resting on top of a cylinder of radius 4 cm and height 10 cm, with labeled dimensions.$

A hemisphere of radius 4 cm is placed on top of a cylinder of radius 4 cm and height 10 cm. What is the total volume?

$\frac{608\pi}{3}$ cm³

$\frac{416\pi}{3}$ cm³

$\frac{736\pi}{3}$ cm³

$160\pi$ cm³

$A rectangular prism 12 cm by 8 cm by 8 cm with a cylindrical hole of radius 2 cm drilled through its full length.$

A rectangular prism is 12 cm long, 8 cm wide, and 8 cm tall. A cylindrical hole with radius 2 cm is drilled through the entire 12 cm length. What is the remaining volume in cubic centimeters? Round to the nearest whole number.

$A hemisphere of radius 4 cm on top of a cylinder of radius 4 cm and height 10 cm, with exterior surfaces highlighted and the hidden contact areas at the joint shown in gray.$

A hemisphere of radius 4 cm sits on top of a cylinder of radius 4 cm and height 10 cm. What is the total exterior surface area?

$128\pi$ cm²

$160\pi$ cm²

$144\pi$ cm²

$112\pi$ cm²

$A cone of radius 3 cm and slant height 5 cm on top of a cylinder of radius 3 cm and height 7 cm, with dimensions labeled.$

A cone with radius 3 cm and slant height 5 cm sits on top of a cylinder with radius 3 cm and height 7 cm. What is the total exterior surface area? Express your answer in terms of $\pi$ .

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